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Esihlokweni esilandelayo uzofunda konke mayelana Ubani Osungule Izibalo, into etholakala njengamanje kukho konke okuthinta impilo yomuntu, ikakhulukazi ibhizinisi nomnotho womuntu, inkampani noma isizwe imbala. Thola ukuthi Ubani Osungule Izibalo?
Ubani Owasungula Izibalo?
Singagomela ngokuthi abaseGibhithe lasendulo baba abasunguli abakhulu besayensi yezibalo. Naphezu kweqiniso lokuthi, njengoba kuvame ukwenzeka ezimweni eziningi, akekho umuntu noma usuku olungasungulwa futhi olubonisa ukuthi Ubani Osungule Izibalo, ngoba le sayensi isiphenduke inguquko enengqondo yempucuko ngokuhamba kweminyaka.
Ngenxa yalesi sizathu, akunakwenzeka ukunikeza impendulo ecacile embuzweni othi Ubani Osungule Izibalo nokuthi isetshenziswa ngamuphi unyaka. Njengoba sesishilo, Ukwengeza kanye Nokukhipha sekuneminyaka eminingi kukhona. Kuthiwani, uma kungase kuqinisekiswe, ukuthi labantu basendulo I-Egypt waqala ukusebenzisa imisebenzi yezibalo ye-arithmetic yobunzima obuthile.
Ngokwesibonelo, bonke base beyazi kakade indlela ababengenza ngayo izibalo ezilula, njengoba kungase kuboniswe ngephepha le- papyrus abalishiya nezichasiselo zangaleyo nkathi futhi elivikelwe okwamanje emnyuziyamu.
Sengiphetha, ubani owasungula izibalo? Singathi njengoba sesike sachaza akekho umuntu othize noma umuntu obongwa ngokudala le sayensi yezibalo. Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics singaba usizo olukhulu kuwe, sikumema ukuthi ufunde konke mayelana nezibalo. Umlando Womshini Wokubhala.
Iyini iMathematika?
Uma kukhulunywa ngezibalo, kubhekiselwa ochungechungeni lwezilimi ezisemthethweni, eziqala ku-axioms futhi zihlale zithobela lokho obekucatshangwa okunengqondo, zisebenze ukuhlela nokuxazulula izinkinga ezahlukahlukene, ngaphakathi kwaloluhlaka lwalokho okushiwo. izingqikithi.
Lokhu kumane kusho ukuthi izibalo ziqukethe uchungechunge lwemithetho ehlelekile, okusho ukuthi, i-abstract, enezela ezintweni ezisezingqondweni zabantu, ukuthi izinombolo zinjani, ama-engeli anjani, ukuthi izimo zejometri zinjani, phakathi kokunye. Isayensi yezibalo inesibopho salokhu:
- Isakhiwo
- I-oda
- I-accounting
- Isilinganiso noma Incazelo Yezinto
Nokho, akuwona umbuzo wokuthi ziyini, nokuthi zakhiwe ngani, noma ngisho nezinhlobo ezahlukene zezici zendawo yonke. Ucwaningo lwesayensi yezibalo lumane luqukethe lokho okuvame ukubandakanya konke okuhlobene nokuqonda izinombolo zesistimu yokucabanga okunzima, wathi uhlelo yilona oluhlanganisa kokubili ama-axiom kanye nama-theorems agcina ethathwe kuwo. bona.
Kucatshangwa ukuthi, kanye nolimi lomlomo, isayensi yezibalo imvamisa ingelinye lamathuluzi engqondo anamandla, abanzi kakhulu futhi ayinkimbinkimbi kakhulu achazwe ngumuntu. Konke lokhu kuwulwazi olubalulekile ukwazi ukuthi ubani owasungula izibalo.
Ingabe Isayensi?
Izibalo yilezo ezikhuluma ngezinto ezifanele hhayi izinto eziyiqiniso. Izibalo zifana nekilasi lesayensi elisemthethweni. Uma sikhuluma “ngokwakha” sisho ukuthi iphethe izinto ezifanele futhi, njengoba sishilo, hhayi izinto zangempela. Ezinye izinto ezifana nalezi:
- Amafomu eJiyomethri
- Izimpande zesikwele
- Izinombolo, phakathi kwabanye
Ngokuvamile akuzona izinto umuntu angazithatha noma azinyakaze, kodwa kuyithuluzi lengqondo. Izibalo njengalezo zinengqondo uma zisohlelweni lwazo lokusebenza, okungukuthi, esimweni sazo esinikezwe sona sokuminyanisa.
Kodwa-ke, izibalo nazo ziwuhlobo lwesayensi olunembile, njengoba zisingathwa ngokunemba. Umphumela otholakala ekusebenzeni kokubala, ukunikeza isibonelo, uzofana ngaso sonke isikhathi uma wenziwa ngendlela efanele, kungakhathaliseki ukuthi ubani owenze, kuyiphi indawo futhi ngayiphi injongo. Konke lokhu kubalulekile ukwazi ukwazi ukuthi ubani owasungula izibalo.
Yiziphi Isayensi Esebenzisa Izibalo?
Imvamisa zonke isayensi yezenhlalo kanye neqondile ziphuma kwizibalo ukuze ziveze okwazo okuqukethwe kanye nobudlelwano. Kusukela emagatsheni we:
- Ubunjiniyela
- ibhayoloji
- I-Chemistry
- I-physics
- Isayensi yezinkanyezi
- Ikhompyutha
IMathematika iqukethe isisekelo esibalulekile futhi iyingxenye yohlobo olufanayo lolimi oluhlelekile, nangaphakathi kwalokhu:
- Isayensi yezokuhlalisana kwabantu
- Izakhiwo
- Ukuma komhlaba
- I-Psychology
- Imidwebo yezithombe
Lapho beza ukuzodlala indima enqumayo neqondile emphakathini uwonke. Sithemba ukuthi le ndatshana yokuthi ngubani owasungula izibalo izoqhubeka nokukuthakasela, futhi sikumema ukuthi uvakashele indatshana yethu ethi The Umlando Wekhadi Lesikweletu.
Umlando Wezibalo
Konke okuhlobene nokuthi uyini umlando wezibalo kuqala ngengxenye yokuhlaziya ezimisweni zayo ekutholakaleni kwezibalo, kanye nasekutholeni izindlela ezehlukene zokuguquguquka kwamatemu futhi ngendlela efanayo kuyizinga elithile, bonke labo ngqondongqondo abakhulu bezibalo ezihlobene nayo.
Ukukhula kwezibalo emlandweni wesintu kuhlotshaniswa eduze nokuthuthukiswa kwegama lezinombolo, uhlobo lwenqubo eyenzeka ngokuqhubekayo emiphakathini eyahlukene yasendulo.
Naphezu kweqiniso lokuthi baba nekhono elithile lokulinganisa ubukhulu nobukhulu, kusukela ngaleso sikhathi babengenawo umbono wenombolo. Ngale ndlela, izinombolo ezingaphezu kuka-2 noma 3 zazingenalo igama njengoba zisebenzisa izinhlobo ezithile zezinkulumo ezilingana nokuthi "eziningi" ukuze zibhekisele kusethi enkulu kakhulu.
Isinyathelo esilandelayo kulolu hlobo lwentuthuko siwukuba khona kokuthile okusondele kakhulu kuthemu yenombolo, nakuba iyisisekelo kakhulu, nakuba kungesona isigaba sebhizinisi esingaqondakali, kodwa njengohlobo lwesakhiwo noma isici sesethi ethile. . Kamuva, ukuthuthukiswa kobunzima besakhiwo senhlalo kanye nobudlelwane baso kungabonakala kuboniswe kulokho okushiwo ukuthuthukiswa kwezibalo.
Izinkinga okufanele zixazululwe seziyinkimbinkimbi kakhulu futhi akusanele ngokwanele, njengoba kwakunjalo emiphakathini yakudala, kufanele nje ubale zonke izinto futhi uphathe ukuxhumana nabanye ngekhadinali yesethi e akubalwanga, kodwa ngendlela efanayo kwaba okuyisisekelo ukukwazi ukubala kwisethi enkulu kunazo zonke ngesikhathi ngasinye, ngesikhathi esifanayo ukulinganisa isikhathi, ukusebenza nezinsuku, ukunika amandla ukubalwa kokulinganisa kulokho okuyiyo. umhwebi.
Ngaphambi kokuthi kufike iNkathi Yesimanje kanye nokusabalala kolwazi emhlabeni wonke, izibonelo ezingatholakala zentuthuko yezibalo ziphakanyiswa izikhathi ezimbalwa kuphela. Imibhalo yezibalo emidala kakhulu engase itholakale yileyo ebonakala ibhalwe eThebuleni elenziwe Ngobumba Plimpton kusukela ngo-1900 ngaphambili Kristu, iyatholakala futhi:
- El eMoscow papyrus kusukela ngonyaka we-1850 ngaphambili Kristu.
- El i-papyrus kusukela ngonyaka we-1650 ngaphambili Kristu.
- I-Los Imibhalo yeVedic Shulba Sutras kusukela ngonyaka wama-800 ngaphambili Kristu.
Ngokujwayelekile, sekucatshangwa ukuthi isayensi yezibalo isivele yavela ekupheleni kokwenza izibalo ngaphakathi kwezentengiselwano, ukuze ukwazi ukwazi isilinganiso soMhlaba futhi ngesikhathi esifanayo ukubikezela konke okuzayo kwesayensi yezinkanyezi. imicimbi. Uthe izidingo ezi-3 zingahlotshaniswa ngandlela thize kulokho okuhlukaniswa iziqephu okubanzi kwezibalo ngaphakathi kocwaningo lwesikhala, ushintsho kanye nesakhiwo.
Kokubili izibalo zaseBabiloni kanye nezaseGibhithe yizona ezapheleliswa kakhulu yisayensi yezinombolo zamaGreki uqobo, lapho zonke izindlela zingachazwa, ikakhulukazi ukuthi kuyini ukufakwa kokuqina kwezibalo ebufakazini obuhlukene kanye nokuqukethwe kwesayensi eshiwoyo nakho. enwetshiwe. Konke lokhu kuyingxenye yomlando kanye nokuthi Ubani Osungule Izibalo.
I-Evolution yayo ngesikhathi
Ukweqa okukhulu kokuziphendukela kwemvelo kanye nolwazi lwezibalo kwenziwa impucuko yamaGreki ngezikhathi ze Ama-Pythagoras ikakhulukazi phakathi kweminyaka engama-569 kuya kwengama-475 ngaphambili Kristu. Isihluthulelo salokhu kungenxa yokuthi baqala ukufunda izinombolo njengezinhlobo zezinto ezingabonakali futhi abazange bakwenze lokho njengesigaba sokumelela izinto zangempela. Uma unentshisekelo esihlokweni sethu esithi Who Invented Mathematics, sikumema futhi ukuthi ufunde mayelana Umlando wezinombolo.
Kwakunezinhlobo zemithetho okwakuyizona ezaziphethe yonke into engumhlaba wezinombolo futhi le mithetho yayikwaziwa. Lapho bekubona, kwethulwa umhlaba omkhulukazi owawungase uhlolwe. Kwakuwumkhathi ongabonakali, nokho, wawuwusizo kakhulu lapho ubuyela ekuphileni kweqiniso.
Cishe ngesikhathi esifanayo, okwakuyikhulu lesihlanu ngaphambili Kristu, amaNdiya nawo ayehlanganyela ekuthuthukisweni okukhulu kanye nezibalo. Kodwa, ngesikhathi esifanayo, bazithola sebelwa nemiqondo efana nenombolo ethi Pi “π” noma endabeni yokungapheli “∞”, izinto ezazingaphezu kwezibalo ezilula ezenziwa abanye abathengisi.
Nokho, ngemva kokuphila isikhathi sodumo olumangalisayo, izibalo zahlala zimile cishe iminyaka eyinkulungwane. Ngaphandle kwempucuko yama-Arab kanye nentuthuko eza ukuzoyenza ku-algebra, ezifundeni zase-Europe izibalo zazilinganiselwe kulezo ezazitholwe amaGreki Asendulo futhi zaqhubeka ngale ndlela kwaze kwaba yisikhathi seRenaissance. Lokhu kubalulekile ukwazi ngokuthi ubani owasungula izibalo.
Umlando wokuqala
Esikhathini esidlule sobufakazi obuyinhloko bemibhalo, kunezinhlobo ezithile zezibalo okuyizona ezibonisa uhlobo oluthile lolwazi lwezibalo eziyisisekelo kanye nesilinganiso sesikhathi esimiswa ezinkanyezini zendawo yonke.
Ukwenza isibonelo, ochwepheshe abaziwa ngokuthi ama-Paleontologists bakwazile ukuthola amatshe e-ocher ngaphakathi I-Blombos Cave etholakala ezifundeni zaseNingizimu Afrika ezisukela eminyakeni eyizinkulungwane ezingama-70 edlule, ezihlotshiswe ngohlobo oluthile lwemifantu enomumo wamaphethini wejometri.
Ngokufanayo, ezinye izinhlobo zezinto zobuciko zemvelaphi yangaphambi komlando zachazwa ezifundeni zaseFrance nase-Afrika, ezineminyaka engaphezu kwezinkulungwane ezingama-35 nezingama-20 ubudala ngaphambili. Kristu, ezisikisela nokuba abanye bazame ukulinganisa isikhathi. Kunobunye ubufakazi bokuthi abesifazane beza ukuzosungula indlela yokugcina uhlobo lwerekhodi lomjikelezo wanyanga zonke ngale ndlela elandelayo:
Cishe amamaki angama-28 noma angama-30 enziwa etsheni noma ethanjeni, kwase kwenziwa uphawu olukhethekile kulo. Ngaphezu kwalokho, abelusi nabazingeli babevame ukusebenzisa imiqondo ka-1 no-2 nabaningi, kanye nomqondo wokuthi akekho noma u-zero (0), lapho bekhuluma ngemihlambi yezilwane.
El Ishango Bone, esitholwe eduze kwe Umfula iNayileikakhulukazi enyakatho-ntshonalanga ye Congo, ingase ibe nobudala obungaphezu kweminyaka eyizinkulungwane ezingu-20 ngaphambili Kristu. Uhlobo lokuhumusha oludumile ukuthi leli thambo liza ukuze sicabange uhlobo lobufakazi obudala kakhulu obungaziwa mayelana nokulandelana kwezinombolo zokuphindaphinda ngokuphinda kabili kanye nezinombolo eziyinhloko. Sithemba ukuthi lesi sihloko mayelana nokuthi ngubani owasungula izibalo sizokuthakasela. Sikumema ukuthi ubone isihloko sethu ku- Umlando Webhalbhu Lokukhanya.
Ukuguga
Izibalo zaseBabiloni, ezibizwa nangokuthi i Izibalo zase-Asiriya-iBabiloni Ziqukethe iqoqo lolwazi lwezibalo oluze lwathuthukiswa ngabantu base-Peoples of Mesopotamia, okumanje Iraq, kusukela empucukweni yokuqala yaseSumeri kuya kulokho okwaba ukuwa kwesikhulu IBabiloni ngonyaka wama-539 ngaphambili Kristu.
Isayensi yezibalo yaseBabiloni ayizange ibe khona emlandweni wezibalo phakathi nalokho okwaba inkathi yamaGreki. Kusukela ngaleso sikhathi izibalo zabo zahlanganiswa nesayensi yamaGreki kanye neyabaseGibhithe ukuze ngaleyo ndlela kusungulwe isayensi yezinombolo yamaGreki.
Esikhathini esithile kamuva, ngesikhathi sombuso wama-Arab, izifunda ze Mesopotamia, indawo ye-hegemonic yophenyo lwale sayensi. Imibhalo yabaseBabiloni ngokwezibalo ivamise ukuba mikhulu kakhulu futhi ihlelwe kahle kakhulu; Lezi zingahlukaniswa zibe izinhlobo ezi-2 zezikhathi okuyizi:
- olumayelana ne I-Antigua IBabiloni phakathi neminyaka ka-1830 kanye no-1531 ngaphambi kokuzalwa kukaKristu.
- Okuphathelene ne I-Seleucid yekhulu lokugcina lama-3 noma ama-4 ngaphambili Kristu.
Ngokuqondene nokuthi uyini umongo, kukhona ukuqhathanisa okumbalwa okuhlukile phakathi kwamaqoqo ama-2 wemibhalo. Izibalo zabaseBabiloni zahlala zingashintshile, ngokokuqukethwe kanye nomlingiswa, cishe iminyaka eyi-2. Uma kuqhathaniswa nemithombo ephansi yezibalo yabaseGibhithe, ulwazi lwamanje lwezibalo lwabaseBabiloni luvela ezibhebheni ezingaba ngu-400 ezenziwe ngobumba, ezambiwa ngonyaka ka-1850.
Zazilandelelwa ngombhalo we-cuneiform, izibhebhe zaziqoshwa ubumba lusamanzi, bese luqiniswa ngokulufaka kuhhavini noma ngokulufudumeza elangeni.
Ubufakazi bokuqala bezibalo obabhalwa phansi yibo obubuyela emuva kumaSumer asendulo, okungabantu abasungula impucuko yokuqala Mesopotamia. Laba bantu baseSumeri babenomthwalo wemfanelo wokwakha uhlobo lwesistimu eyinkimbinkimbi ye-metrology kusukela ngonyaka wezi-3.000 ngaphambili. Kristu.
Kusukela cishe ngonyaka wezi-2.500 ngaphambili Kristu, Kusukela ngaleso sikhathi kuqhubeke, impucuko yaseSumeri yafika izobhala lokho okwaziwa ngokuthi amatafula wokuphindaphinda anyatheliswe etafuleni elenziwe ngobumba futhi ngesikhathi esifanayo bazama ukufeza izinkinga zejometri kanye nokuzivocavoca kokuhlukanisa. Izibonelo zakuqala zezinombolo zaseBabiloni yilezo nazo ezangesikhathi esifanayo. Ngakho-ke ngubani owasungula izibalo ziyingxenye eyisisekelo yabantu abaningi.
I-Egypt
Lezi zibalo yizona ezakha into eyaziwa ngokuthi yigatsha elathuthuka kakhulu ngezikhathi ze- IGibhithe lasendulo nangolimi lwabo.
Kusukela kulokho okwakuyinkathi yobuGreki, ulimi lwesiGreki lwaba olwalandelayo olwathatha indawo yaseGibhithe njengolimi olwaqala ukubhalwa ochwepheshe baseGibhithe futhi kusukela ngaleso sikhathi, izibalo zabo zahlanganiswa nezamaGreki futhi neyabaseBabiloni ukuze ikwazi ukuzala amaGreki.
Ucwaningo lwezibalo ezifundeni zase-Egypt lwaqhubeka kamuva ngaphansi kwalokho okwakuyithonya lama-Arabhu njengengxenye yezibalo ze-Islamic, lokhu kwenzeka ngesikhathi lapho ulimi lwesi-Arabhu lukwazi ukuba ulimi lokubhala kakhulu lwazo zonke izingane zesikole zaseGibhithe. .
Imibhalo yezibalo emidala kunayo yonke yaba yileyo etholakala ku-a eMoscow papyrus, ezinomlando olinganiselwe woMbuso izindlela de I-Egypt, phakathi neminyaka engu-2.000 no-1.800 ngaphambili Kristu. Njengenani elikhulu lemibhalo yakudala, equkethe lokho okwamanje okwaziwa ngokuthi:
- izinkinga zamagama
- izinkinga ngomlando
Ukuthi banenhloso eyodwa kuphela yokuzijabulisa. Sekucatshangwa ukuthi i-1 yalezi zinkinga ezibaluleke kakhulu futhi ebaluleke kakhulu ngoba kufanele inikeze uhlobo lwendlela yokuthola umthamo we-trunk, yiyona ethi:
“Uma kufanele bakutshele: Ngokuba nephiramidi elisikiwe elingu-1 (elinesisekelo esiyisikwele) elingu-6 ubude elinesakhiwo esiqondile, ngo-4 esisekelweni (sikhuluma ngesisekelo esingezansi, okungukuthi, ingxenye engezansi) futhi okungu-2 phezulu (sisho isisekelo esiphezulu). Kuphi:
- Uthola ukwenza isikwele sika-4 futhi siphumela ku-16.
- Bese uphinda u-4 bese uthola u-8.
- Bese wenza isikwele sibe ngu-2 futhi kufanele sibe ngu-4.
- Bese wengeza u-16, futhi 8 futhi kamuva 4 bese uthola 28.
- Bese uthatha 1/3 kokungu-6 futhi lokhu kuphumela ku-2.
- Manje ubamba ama-28 cishe izikhathi ezi-2 futhi umphumela uba ngu-56.
Ekugcineni, yonke le nkinga iholele ku-56. Ngakho-ke uthole into efanele kule nkinga”
Ngaphakathi kwayo le Papyrus yilapho kunesethi yemithetho esebenza ukuze ikwazi ukunquma umthamo noma ubukhulu bento efana nebhaluni. Manje kukhona enye into ethathwa njengobufakazi bezibalo zasendulo ezibalulekile futhi sikhuluma ngayo i-papyrus kusukela ngonyaka we-1650 ngaphambili Kristu. Lolu wuhlobo lwe-geometry kanye ne-arithmetic imiyalelo yemiyalelo.
Sengiphetha, leli thuluzi yilona elenza kube lula izinyathelo zokuthola isisombululo sezindlela kanye nezindawo zokuphindaphinda ezindaweni ezahlukahlukene. Ngendlela efanayo, yiyona enobufakazi bolunye ulwazi lwezibalo lwabaseGibhithe, okuhlanganisa:
- Izinombolo Eziyinhloko Nezihlanganisiwe
- I-Arithmetic Mean
- ijiyomethri
- i-harmonica
- Ukuqonda Okulula kwe Imfumbe ka-Eratosthenes
- Theory of Perfect Numbers "ukwazi, inombolo 6".
Le papyrus futhi ikhombisa ukuthi kungenzeka kanjani ukuxazulula lezo zibalo zomugqa we-oda loku-1, kanye nochungechunge lwejometri nochungechunge lwe-arithmetic. Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics siyakuthakasela, sikumema ukuthi uvakashele isihloko sethu mayelana I-Historia de Microsoft.
Greece
Iqukethe izibalo eziye zabhalwa ngolimi lwesiGreki kusukela ngonyaka ka-600 ngaphambili Kristu kuze kube unyaka wama-300 ngemva kwalokho Kristu. Izazi zezibalo zamaGreki zazihlala ezindaweni noma abantu abahlakazeke kuzo zonke izifunda ze IMedithera NOMAempumalanga, kusukela ezindaweni ze Italia kuze kube I-North Africa, nokho, babehlanganiswe ulimi olufanayo nayisiko elivamile.
Lonke uphenyo olukhona lwezibalo zangaphambi kwe-Hellenistic luza ukuze lubonise ukuthi kuyini ukusetshenziswa kwe-inductive reasoning, lokhu kusho ukuthi kuwukubhekwa okuphindaphindiwe okusetshenziselwa ukumisa imithetho evamile.
Izazi zezibalo zamaGreki, ngokungafani nalezo ezandulele, zasebenzisa lokho okuwukucabanga okunciphisayo. Izibalo zamaGreki zasebenzisa ingqondo ukuze zikwazi ukudonsa eziphethweni, noma izithiyori, ezincazelweni nama-axiom. Umbono olula wezibalo njengohlobo lwenethiwekhi yethiyori ukuthi zisekelwa ama-axiom acacile ezinhlobonhlobo ezahlukahlukene. Izakhi zika-Euclid kusukela ngonyaka wama-300 ngaphambili Kristu.
Ngokuvamile kunenkolelo yokuthi izibalo zamaGreki zaqala ngabakhulu nabaziwayo Amazwi de IMilethu cishe ngonyaka wama-624 noma wama-546 ngaphambili Kristu, futhi futhi Ama-Pythagoras eminyakeni engama-582 no-507 ngaphambili Kristu. Nakuba kungase kuxoxwe ngazo ngohlobo lobubanzi bethonya labo, ziye zafana, ngokunokwenzeka zikhuthazwa izibalo ezihlukahlukene zabaseGibhithe, kanye namaNdiya nabaseMesophothamiya.
Ngokwenganekwane exoxwayo, le ndoda okuthiwa uPythagoras yafika ukuze izovakashela izifunda zaseGibhithe ukuze ifunde izibalo, isayensi yezinkanyezi kanye ne-geometry kubo bonke abapristi baseGibhithe.
UThales waseMilethu wayengumuntu owayesebenzisa i-geometry ukuze akwazi ukuxazulula izinkinga ezahlukene njengezinxushunxushu zokubala ubude bemibhoshongo kanye nebanga imikhumbi enalo ukusuka ogwini. Omunye umlingiswa kuthiwa, njengoPythagoras, isigaba sokuqala sokuboniswa kwethiyori enegama lakhe ngokuqondile, naphezu kokuthi isitatimende sethiyori sinomlando omkhulu.
Okubhalwe kumazwana owenziwe ngu I-Euclid,kukhale indoda I-Proclus nguye othi omunye umlingiswa uqanjwe igama Ama-Pythagoras wafika ekuvezeni inkolelo-mbono ebizwa ngegama lakhe futhi yiyona eyakha i-algebra ye-Pythagorean kathathu ngaphambi kokuba ibe ngokwejometri. I Plato's Academy njalo nginesiqubulo esithi:
"Makungadluli muntu ongayazi iGeometry"
Okubizwa ngokuthi AmaPythagoreans babenomthwalo wemfanelo wokufakazela ukuba khona kwezinombolo ezingenangqondo. Kwakukhona indoda eyakhula phakathi neminyaka engama-408 kuya kwengama-355 ngaphambili Kristu indlela ebizwa ngokuthi exhaustive method eyenziwa ngu I-Eudoxus, okwaba umgqugquzeli obaluleke kakhulu wokuhlanganiswa kwesimanje.
Okukhulu I-Aristotle phakathi neminyaka engama-384 kuya kwengama-322 ngaphambili Kristu, waba ngumuntu wokuqala ukuyithatha kalula imithetho yengqondo emlandweni wesintu. Kamuva, kwakukhona umuntu owafika ngaphambili kakhulu ukuzonikeza isibonelo sendlela yezibalo esetshenziswa namuhla futhi lokhu kwakungeyona into futhi akukho okuncane kunalokho. I-Euclid, ukwenze nge:
- I-Axioms
- Amathiyori
- Izincazelo
- Izikhombisi
Ngokunjalo, weza ukuzokwenza izifundo ze-conic mathematics. Incwadi ka I-Euclid enesihloko "Izinto” yiyona eqoqa zonke izibalo ezihlobene naleso sikhathi. Kule ncwadi yeIzinto” izinhlobo ezihlukahlukene zezinkinga zezibalo ezibalulekile zivame ukubhekwana nazo, naphezu kweqiniso lokuthi ngaso sonke isikhathi kwenziwa ngaphansi kwesigaba solimi lwejometri. Ngakolunye uhlangothi, ngaphezu kwezinkinga ezahlukene zejometri, iphinde ibhekane nezinkinga ze-arithmetic, algebraics futhi, ekugcineni, ukuhlaziywa kwezibalo ngokujwayelekile.
Ngakolunye uhlangothi, ngaphandle kwama-theorems ajwayelekile abhekisela ku-geometry, njengecala lika Umbono kaPythagoras, the Izinto (incwadi) ihlanganise nohlobo lobufakazi bokuthi impande yesikwele ka-2 imane iyinombolo engenangqondo futhi enye imayelana nokungapheli kwezinombolo eziyinhloko. Umbhalo ka-Eratosthenes othi Sieve phakathi nonyaka ka-230 ngaphambi kukaKristu, wasetshenziswa kulokho kamuva okwaba ukutholakala kwezinombolo eziyinhloko.
I-Gran Bretaña
Izikhumbuzo ezinkulu ze-megalithic ezifundeni ze E-England futhi ku IScotland, phakathi nalokho okwakuyinkulungwane yesithathu ngaphambili Kristu, yizona ezingahlanganisa imibono eminingi yejometri njengendaba yendilinga, Ellipses futhi i I-Pythagorean kathathu ekuchazeni kwayo. Kulezi zifunda, futhi, abaningi babezibuza ukuthi ubani owasungula izibalo.
China
Umbusi odumile we China kubizwa UQin shi huang wayengumuntu owayala phakathi nonyaka ka-212 ngaphambi kukaKristu ukuthi zonke lezo zincwadi ezingakhishwanga umbuso Qiniso zashiswa. Lesi sinqumo asizange samukelwe yibo bonke abantu, nokho, ngenxa yalokhu, kuncane kakhulu okwaziwayo mayelana nezibalo ezifundeni zezifunda. IsiShayina sasendulo.
Incwadi yezibalo endala kunazo zonke eyasinda kulesi simemezelo esishisayo yileyo enesihloko esithi "I Ching”, okuyilona elisebenzisa ama-trigrams kanye nama-hexagrams anenjongo yefilosofi, kanye nezibalo futhi ekugcineni angaqondakali. Lezi zinto zezibalo zihlanganiswa emigqeni ephelele noma ehlukene ebizwa ngokuthi "Yin” okuyingxenye “yowesifazane” kanye “Yang” okuyingxenye yesilisa, ngokulinganayo.
Emidala kunayo yonke ekhuluma ngejiyomethri ezifundeni ze China kuba yilokho okuvela ku-a I-Mohist Philosophical Canon, kusukela ngonyaka wama-330 ngaphambili Kristu, eyaqoqwa yi ama-acolyte de Mozi phakathi neminyaka engama-470 nama-390 ngaphambili Kristu. Okuthiwa Mo Jing nguye owachaza izici eziningi zemikhakha ehlukahlukene ehlotshaniswa nesayensi yezemvelo kanye nalowo owanikeza isilinganiso esincane sezibalo.
Ngemva kokushiswa kwezincwadi, inzalo ebusayo phakathi neminyaka engu-202 ngaphambi kukaKristu neyama-220 ngemva kukaKristu, yaqala ukuchaza izincwadi ezihlukahlukene eziphathelene nalezi zihloko ze-algebra okungenzeka zazigcwele imisebenzi okwafinyelelwa kuyo.
Esinye sezigqame kakhulu esakhiqizwa yileso esinesihloko esithi “Izahluko Eziyisi-9 Zobuciko Bezibalo”, isihloko saso esiphelele savela phakathi nonyaka ka-179 ngemva kwalokho. Kristu, nokho, kwakukhona ezinye izihloko zeminye imisebenzi ngaphambi kwalokho ezansi. Lo msebenzi yilowo obhekana nezinhlobo zezinkinga ezingaba ngu-246 ezivame ukubandakanya imikhakha efana nale:
- Ezolimo
- Ibhizinisi
I-Geometric Isebenzisa ukuze ukwazi ukusungula ubukhulu obuhlukene be:
- AmaPagoda
- Ubunjiniyela
- ukuhlola
Imibono emayelana "Nonxantathu Wakwesokudla" kanye "Ne-Pi". Okunye okusetshenzisiwe yilokhu okubizwa Isimiso sikaCavalieri emiqulwini engaphezu kweminyaka eyi-1.000 ngaphambi kwayo Knights Bengizoyibumba ezindaweni ze ENtshonalanga.
Kamuva, kwavezwa ubufakazi mayelana nalokhu Umbono kaPythagoras kakade uhlobo lwenqubo yezibalo ekuqedeni Gauss-Jordan. Kwafika umuntu ezosho okuthile ngalo msebenzi phakathi nekhulu lesithathu leminyaka, lo muntu wabizwa U-Liu Hui. Konke lokhu kuyingxenye yalabo abasungula izibalo.
Sengiphetha, imisebenzi yezibalo yesazi sezinkanyezi u-Han nomsunguli oqanjwe ngaye UZhang Heng phakathi nonyaka wama-78 no-139 ngemva kukaKristu, yiyona eyayiqukethe isigaba sokwakheka kwe-“pi” ngendlela efanayo, okuyiyona eyahluka ngezibalo zayo siqu. U-Liu Hui.
Ubani omunye owasebenzisa ifomula yakhe ethi "pi" ukuze akwazi ukwenza izibalo ezihambisanayo. Kwatholakala nezincwadi ezabhalwa abadumile Jing Fang phakathi nonyaka wama-78 – 37 ngaphambili Kristu; ngokusebenzisa ukhefana wePythagorean, kanjalo I-Jing wakwazi ukubona ukuthi izingxenye zesihlanu eziphelele ezingaba ngu-53 zazicishe zibe yisishiyagalombili.
Yilokhu kamuva okwakuyoholela ekutholakaleni okukhulu kwesimo somoya, njengoba nje sahlukanisa esesishiyagalombili sibe izingxenye ezilinganayo ezingu-53, futhi sasingeke sibalwe kabusha ngokunemba okukhulu kwaze kwaba phakathi nekhulu le-XNUMX, indoda eyaziwayo yomdabu waseJalimane okuthiwa. Nicholas Mercator. Kulezi zifunda kwaphakama umbuzo omningi: Ubani owasungula izibalo? Njengoba ongoti abaningi bethi kuqhamuka kuleli zwe abathi isayensi yaphuma.
India
Izibalo zase-Indian noma izibalo zamaHindu zizuze ukubaluleka okukhulu kusiko laseNtshonalanga langaphambi kweNkathi Yenguquko ngefa lezinombolo zalo, okuhlanganisa uziro wenombolo (0), ukukhombisa ukungabikho kweyunithi ekubhalweni kwendawo.
Izibalo zokuqala ezaziwa emlandweni waseNdiya yilezo ezisukela ngonyaka wezi-1 - 3.000 ngaphambili. Kristu, etholakala ku I-Indus Valley Culture okungokwempucuko Harappa etholakala enyakatho ye India futhi of Pakistan Njengamanje.
Lolu hlobo lwempucuko lwaluphethe ukuthuthukisa uhlobo lwesistimu yezilinganiso kanye nezisindo ezifanayo ezazisebenzisa lokho okuyisimiso sedesimali, ubuchwepheshe obuthuthuke kakhulu obunezitini ezithile ezimelela izilinganiso, njengemigwaqo ehlelwe ngama-engeli aphelele futhi aqondile futhi. isethi yomumo wejometri kanye nomklamo, ohlanganisa:
- Cuboid
- Imiphongolo
- Izigaxa
- Amasilinda
- Imiklamo Yendilinga
- Idizayini ye-Concentric kanye ne-Secant Triangles.
Izinto zezibalo ezisetshenziswayo zafinyelela ekuhlanganiseni umthetho wedesimali ogcina isikhathi onezinhlobo ezithile zokuhlukaniswa okuncane nokunembayo, kanye nezinhlobo ezithile zezakhiwo ezisebenza ukukala kusukela ezingxenyeni eziphelele eziyi-8 kuye kweziyi-12 zomkhathizwe kanye nesibhakabhaka futhi ngokufanayo. indlela ithuluzi elisebenzela ukukalwa kwezindawo zazo zonke izinkanyezi eziqashelwa ukuzulazula.
Ukubhalwa kwamaHindu ngokunokwenzeka akukakahunyushwa kuze kube manje, yingakho luncane kakhulu ulwazi mayelana nezindlela ezilotshwe futhi eziphathelene nezibalo Harappa. Kunobufakazi bemivubukulo obenze ososayensi abaningi basola ukuthi le mpucuko yasebenzisa uhlobo lwesistimu yezinombolo enesisekelo se-octal futhi yayinenani lophawu u-Pi (π), okuyisizathu esiphakathi kobude bomjikelezo nokuthi buyini ububanzi bayo.
Nokho, kwaba phakathi nenkathi yakudala esukela ekhulwini lokuqala kuya kwelesi-XNUMX lapho izazi zezibalo zaseNdiya zikhula. Ngaphambi kwalesi sikhathi, abantu abangamaHindu bahlangana ngandlela thize nezwe lamaGreki. Ukuxoshwa kwe Alejandro Magno mayelana nezifunda ze India kwenzeka phakathi nekhulu lesine ngaphambili Kristu.
Ngakolunye uhlangothi, ukusabalala kweBuddhism ezifundeni ze China futhi lokho kwezwe lama-Arabs yikho okwandise amaphuzu okuxhumana kwezifunda ze India ngengaphandle. Nokho, izibalo zamaHindu yizona ezathuthukiswa endizeni yokuqala, zithembele kakhulu ekubalweni kwezinombolo kunokuqina kokudonswa kwemali.
Intuthuko ehlukahlukene eyenziwe eNdiya kwizibalo ngemuva kwe suba sutras imvamisa I-Siddhantas, okuyimibhalo ethile yezinkanyezi yangaleso sikhathi I-Gupta Ikhulu lesi-XNUMX nelesi-XNUMX ngaphambili Kristu, okumane kubonise ithonya elikhulu lamaGreki kubo.
Lezi zibaluleke kakhulu ngoba ziqukethe isibonelo sokuqala sobudlelwane be-trigonometric obusungulwa ngohlobo lwe-semi-chord, njengaku-trigonometry yanamuhla, esikhundleni sohlobo lwe-chord egcwele, njengoba kunjalo.
Ikholi ISuria - sidhanta phakathi nonyaka wama-400 nguye owangena emisebenzini ye-trigonometric ye i-cosine, webele y i-arcsine futhi ngesikhathi esifanayo weza ukumisa imithetho ukuze kusungulwe imikhondo yazo zonke izinkanyezi ezihambisana nezindlela zazo zamanje esibhakabhakeni.
Leli klasi lomsebenzi lahunyushwa lisuka olimini lwesi-Arabhu layiswa olimini lwesiLatini phakathi nesifundo Iminyaka ephakathi. AmaHindu ayingxenye yabasunguli bezibalo, ngakho embuzweni wethu othi Ubani owasungula izibalo? AmaHindu nawo ayeyingxenye ebalulekile yawo. Bheka isihloko sethu kuUbani Owasungula Ikhampasi?
Inca
Izibalo zempucuko ye-Inca noma ezaziwa kangcono ngokuthi Tawantinsuyu Yilawo abhekisela kusethi yolwazi lwezinombolo kanye nejometri futhi, ngaphezu kwakho konke, kumathuluzi athuthukiswe futhi asetshenziselwa isizwe sama-Inca ngokwawo ngaphambi kokufika kwezifiki zaseSpain.
Ingabonakala, empeleni, ngamandla ayo amakhulu okubala emkhakheni wezomnotho. Okuthiwa yupanas futhi i I-Quipus zingenye yezinkomba ezibaluleke kakhulu izibalo ezikwazile ukuzifinyelela kulokho okuwukuphathwa kombuso we Inca.
Lokhu kwaba enye yezibalo ezilula, nokho, eziphumelela kakhulu, ngezinjongo zokubala, ezisekelwe ohlelweni lwedesimali; ababazi ngayo u-ziro (0) futhi ekugcineni baphumelela:
- Ukwengeza
- Bamba
- Ukuphindaphinda
- Isigaba
Iphinde yaba nesigaba sabalingiswa abasebenzayo abavelele emisebenzini yokulinganisa, izibalo nokuphatha. Okwakukude kakhulu nohlelo luka-Euclid lwezibalo njengohlobo lweDeductive Corpus. Okunamandla ngokuphelele futhi kunenzuzo ezidingweni zokuphatha okumaphakathi kwempucuko.
Ngakolunye uhlangothi, ukucaciswa kwemisele, imigwaqo kanye nezikhumbuzo, njengoba kwenzeka ekuhlelweni kwamadolobha nezinqaba, kwadingeka ukuba kuthuthukiswe isigaba seJiyomethri Esiwusizo, esasibalulekile ekukalweni kwezindawo nobude, ngaphandle nje kokuthi umklamo wezakhiwo. Ngesikhathi esifanayo, bahlakulela amandla abalulekile kanye nezinhlelo zokulinganisa ubude, ezathatha izingxenye zomzimba womuntu njengesigaba sereferensi.
Ngaphandle kwalokhu, beza ukuze basebenzise kahle izinto noma izenzo ezingavumela umphumela ngenye indlela, noma kunjalo, esebenzayo futhi efanelekile. Konke lokhu yikho obekuyingxenye yomlando wezibalo futhi owasungula izibalo.
Maya
Basebenzise uhlobo lwendlela yokubala ye-vigesimal esekelwe ku-20 wempande ehlanganisiwe, iyafana nezinye izakhamuzi zaseMesoamerica. Indlela eyasetshenziswa yenani lamachashazi namadashi, eyayivame ukwakha isisekelo salokho okuyizinombolo zamaMayya, yayisetshenziswa kusukela ngonyaka ka-1.000 XNUMX ngaphambili. uKristu; amaMaya kamuva azokwamukela Late Preclassic, bese wengeza uphawu lukaziro (0).
Lokhu yikhona okungenzeka kube isenzakalo sokuqala nesaziwa kakhulu segama lenombolo enguziro (0) elicacile emhlabeni wonke, nakuba kungenzeka ukuthi landulelwa uhlelo lwaseBhabhiloni. Ukusetshenziswa kokuqala kwegama elithi "0" kwakungenkathi liqoshwa ezikhumbuzo ezinosuku lonyaka wama-357 ngemva kukaKristu.
Ekusetshenzisweni kokuqala kwalokhu, inombolo ethi "0" yayisebenza njengohlobo lwe-positional notation, okusho ukuyekwa kohlobo oluthile lokubala lwekhalenda. Kamuva, ngokuvamile lakhula laba inani elalingase lisetshenziswe ekubaleni, futhi laze lanezelwa emibhalweni ehlukahlukene ye-glyphic phakathi neminyaka engaphezu kuka-1.000 XNUMX, kwaze kwaba yilapho ekugcineni ukusetshenziswa kwalo kushabalala kusetshenziswa iSpanishi.
Ohlotsheni lwendlela yokufaka izinombolo eziyisisekelo, lokho okwaziwa ngokuthi iyunithi imelelwa yiphuzu elingu-1, bese kuthi u-2 (..), 3 (...) no-4 (....) amaphuzu asebenze ngenhloso yokuchaza izinombolo , Ezintathu nezine, kanti kulena enomugqa ovundlile, iyona esebenza ukuze imele inombolo yesi-5.
Phakathi nenkathi ye-Postclassic, uphawu olunesimo segobolondo noma umnenke lumele inombolo "0"; phakathi nenkathi ye-Classic kwasetshenziswa ezinye izinhlobo zama-glyphs. Abantu baseMeya bakwazi ukubhala noma yiluphi uhlobo lwenombolo ukusuka ku-0 kuye ku-19, besebenzisa uhlobo lwengxube yezimpawu ezishiwo.
Inani elinqunyiwe lenombolo yilelo elimiswa ngokuma kwayo mpo; lapho ukhuphuka indawo, inani elibalulekile leyunithi liphindaphindwa ngenombolo engu-20. Ngale ndlela, uphawu oluphansi kakhulu yilolo oluzomelela wonke amayunithi esisekelo, uphawu olulandelayo yilo olusendaweni yesi-2, olumele ukuphindaphinda ngo-20 kweyunithi ngokwayo, futhi uphawu olusendaweni yesi-3 yilolo olumele ukuphindaphinda ngo-400 njalonjalo ngokuphindaphindiwe.
AmaMayya ayimpucuko eyingxenye ebalulekile yabasunguli noma labo abasebenzisa izibalo kusukela ezikhathini zasendulo, ngakho-ke uma uzibuza ukuthi ubani owasungula izibalo? AmaMeya ayingxenye yalokhu.
Iminyaka ephakathi
Ake sibheke kancane ngezibalo kulokho okwakukhona Iminyaka ephakathi, isikhathi lapho ochwepheshe abaningi besayensi babezibuza ukuthi ubani owasungula izibalo nokuthi yaziwa kanjani, nokho, kuseyinto enkulu engaziwa emhlabeni wonke.
izwe lamaSulumane
Izibalo ze-Islam, nazo zaziqashelwa njengama-Arabhu noma njengamaSulumane, zanda ngokuqhubekayo njengoba amaSulumane ngokwawo ethatha isikhundla ezindaweni ezintsha.
Ngejubane elikhulu elingavamile, umbuso wamaSulumane wanwetshwa kuyo yonke indawo ehlelwe ngasogwini lolwandle. IMedithera, kusukela ezifundeni ze iPheresiya uyini umsinga I-Iran kuze kufinyelele Pyrenees. Naphezu kokunqotshwa, waba neqhaza elikhulu ekusizeni izibalo ngekhulu lesi-8.
Njengoba kungase kucatshangwe, ingxenye enkulu yemibhalo yamaSulumane ephathelene nesayensi yezibalo yabhalwa ngolimi lwesi-Arabhu futhi akuyona yonke eyabhalwa ama-Arabhu ngokwawo, njengoba, ngendlela efanayo ulimi lwesiGreki olwafika ngalo. ukuze lisetshenziswe izwe lamaGreki, ulimi lwesi-Arabhu lwaqala ukusetshenziswa njengohlobo lolimi olubhalwayo yizazi ezinkulu ezazingezona ezendabuko yama-Arab kuwo wonke umhlaba omkhulu wamaSulumane ngaleso sikhathi.
https://www.youtube.com/watch?v=M1bpyd-vRXE
Ezinye izazi zezibalo zamaSulumane eziningi zabaluleka kakhulu kanye nama-Arabhu, njengamaPheresiya. Phakathi nekhulu lesishiyagalolunye, indoda eyaziwa ngokuthi I-Al-Juarismi Nguye owafika ezobhala izincwadi ezihlukahlukene ezibaluleke kakhulu mayelana nezinombolo zesi-Arabhu kanye nezindlela ezihlukahlukene zokuxazulula izibalo zezibalo.
Incwadi yakhe, ebhekisela ekubaleni kwama-Arabhu, yabhalwa phakathi nonyaka ka-825, kanye nomsebenzi womunye umlingiswa ogama lakhe lingu. Al Kindi, okwaba amathuluzi abantu okwenza kwaziwe zonke izibalo zesi-Arabhu kanye nalokho okwaziwa ngokuthi izinombolo zesi-Arabhu ezifundeni ze ENtshonalanga.
Igama elithi algorithm yilelo elivela kuLatinization yegama layo, elithi "algoritmi", futhi igama elithi "algebra" lisuselwa esihlokweni somunye wemisebenzi yawo.
Okusho ukuthi ekuhumusheni kwayo "Iqoqo lokubala ngokuqedela nokuqhathanisa". I-Al-Juarismi Waqanjwa ngokujwayelekile waphinde wathathwa ngokuthi "Ubaba we-algebra", lokhu kungenxa yeqhaza lakhe elikhulu nelibalulekile kulo mkhakha ofanayo. Yena ngokwakhe uzele ukuzonikeza umfanekiso ocophelela kakhulu ngesixazululo sezibalo ze-2nd degree ezinezimpande ezinhle, futhi le ndoda yaba ngowokuqala ukwazi ukufundisa abanye i-algebra kanjalo ngendlela yayo ngayinye eyisisekelo.
Ubephinde abe ngumuntu oze ukuzokwethula ukuthi iyiphi indlela ebalulekile ethi "Balance" kanye "nokunciphisa", ebhekisela ekwengezweni kwezakhi ezikhishiwe ezazikolunye uhlangothi lwezibalo, lokhu kusho, ukwesulwa kwemibandela efana nalena. ngakolunye uhlangothi lwe-equation.
Lolu hlobo lokusebenza lwaze lwachazwa kakhulu yi- Al-Jarismi kanye ne i-al-jabr. Okwabaningi kwakumayelana:
“Iqoqo lezinkinga ezingazange zixazululwe, kodwa kunalokho ohlotsheni lokuchazwa oluqala ngezimo ezindala ezivame ukunikezwa kuzo zonke izinhlobo zezibalo ezingenzeka ngeqoqo lezingoma, kusukela kulokho Ngesikhathi esifanayo, i-algebra into yokufunda.
IYurophu ngeNkathi Ephakathi
Ekuhambeni kwe Iminyaka ephakathi ukusetshenziswa kwe-algebra emikhakheni yamabhizinisi, kanye nokuba nekhono kwezinombolo, yikho okwaholela ekusetshenzisweni njalo izinombolo ezingenangqondo, okuwuhlobo lwesiko olube seludluliselwa ezifundeni ze Europa. Ngendlela efanayo, izimpendulo ezingezinhle ku:
- Izinkinga Ezithile
- Amanani Acatshangwayo
- Izibalo zeDegree 3.
Ukuthuthukiswa kwezibalo ngokuhamba kwesikhathi Iminyaka ephakathi wakhuthazwa njalo yilokho okwakuyinkolelo yohlobo oluthile "I-oda Natural”; kwabiza indoda Boethius yiyona eyawabeka ngaphakathi kohlelo lwezifundo, phakathi nekhulu lesithupha, ngokufaka umqondo wokuthi I-Quadrivium ngoba bekuyini isifundo semethodical:
- izibalo
- I-geometry
- Isayensi yezinkanyezi
- Umculo
Kwakuyini eyakheI-arithmetica yesikhungo”, uhlobo lokuhumusha lwe uNicomachus, phakathi kwezinye izincwadi ezaba isisekelo sezibalo kwaze kwaba yilapho sezitholakele zonke izincwadi zezibalo zamaGreki nama-Arabhu.
Ngesikhathi sekhulu leshumi nambili, ikakhulukazi ezifundeni ze Italia futhi ku España, baqala ukuhumusha imibhalo ethile eyayibhalwe ngesi-Arabhu futhi yilapho izibalo zamaGreki zaphinde zatholakala khona. Umlingiswa owaziwa ngokuthi Toledo Iguqulwa ibe uhlobo lwesikhungo samasiko futhi iphinde ibe isikhungo sokuhumusha; izazi zemvelaphi yaseYurophu zathuthela ezifundeni ze España futhi nasezindaweni ze Sicilia ukuze ukwazi ukusesha izincwadi zesayensi zama-Arabhu ezihlanganisa:
"I-Calculus Compendium Ngokuqedwa Nokuqhathanisa"
Yenziwe ngu al-Khwarizmī, futhi babefuna nenguqulo ephelele yencwadi ethi "The Elements" eyabhalwa abadumile I-Euclid, eyahunyushelwa ezinhlotsheni eziningi zezilimi yiqembu lamadoda elibizwa ngokuthi:
- Adeleard of Bath
- UHerman waseCarinthia
- UGerard waseCremona
Ukukhula kwezohwebo nomnotho okwaziwayo ezifundeni ze Europa, ngokufakwa kokuvulwa kwemizila emisha ebheke endaweni esempumalanga yamaSulumane, yilokho okuvumela ngendlela efanayo abathengisi abaningi abahlukene ukuba bakwazi ukuzivumelanisa namasu adluliswa ama-Arabhu ngokwawo. Yonke imithombo emisha iyona ethuthukisa izibalo zalezi zikhathi.
Kwafona indoda I-Fibonacci ungumlingiswa obhala i-"Liber Abaci" yakhe phakathi nonyaka we-1202, owaphinde wakhishwa ngonyaka we-1254, lo ngumbhalo okwazi ukukhiqiza intuthuko yokuqala ebalulekile ngokwezibalo ezifundeni zalo lonke elaseYurophu. ngokwethulwa kohlelo lwezinombolo lwaseNdiya olwaziwayo, njengoba negama libonisa, kwakungeyamasiko amaNdiya ahlanganisa uhlelo lokuphawula ngedesimali, kanye nokuma kanye nokusetshenziswa okukhulu okuvamile kwenombolo enguziro.
Lena kwakuyithiyori eyafika ukufundiswa ku I-Quadrivium, nokho, ngendlela efanayo eyayihloselwe umkhuba wokuhweba. Lolu hlobo lokufundisa lusakazwa ngezingcingo "i-botteghe d'abbaco" ezaziwa ngokuthi "izikole ze-abacus", lapho “amaestri” (othisha) ayephethe ukufundisa:
- izibalo
- I-geometry
- Izindlela zokubala
Kubo bonke labo bathengisi besikhathi esizayo bezikhathi ezizayo, ngezinkinga zokungcebeleka, ezazaziwa kakhulu ngenxa ye-"Algebra Treatises" othisha ngokwabo abebeyishiya kuwo wonke umlando wezibalo. Nakuba i-algebra kanye negatsha le-accounting kuyizo ezihamba ngezindlela ezihlukene, ekwenzeni izibalo eziyinkimbinkimbi ngokuvamile ezihlanganisa inzalo ehlanganisiwe, ukuphatha okuhle kakhulu kwe-Arithmetic kwaziswa kakhulu abaningi.
Konke lokhu kuyingxenye yomlando wezibalo futhi owasungula izibalo njengoba zazisetshenziswa imiphakathi eminingi emandulo. Sithemba ukuthi le ndatshana emayelana nokuthi ngubani owasungula izibalo ikusiza ekutholeni ulwazi olusha, sikumema futhi ukuthi ubone indatshana yethu ephathelene nezibalo. umlando womsakazo.
I-European Renaissance
Kukhona intuthuko enkulu endaweni yezibalo phakathi nekhulu leshumi nane, njengoba kunjalo nge-dynamics of movement. Kwafona indoda Thomas Bradwardine ungowokuqala ukuphakamisa ukuthi ijubane linyuswe ngesilinganiso se-arithmetical njengesizathu sokuthi amandla okumelana akhuphuka ngesilinganiso sejometri, futhi uyaqhubeka nokubonisa imiphumela yakhe ngesethi yezibonelo ezithile, njengoba i-logarithm yayingakafiki. ukucabanga.
Ucwaningo lwakhe luyisibonelo esihle sokuthi indlela yezibalo esetshenziswa ngayo al-Kindi futhi Vilanova ngaleso sikhathi. Izazi zezibalo zangaleso sikhathi, zingenayo imigomo yokubala okuhlukanisayo noma umkhawulo wezibalo, ziyaqhubeka nokuthuthukisa eminye imibono njengoba kunjalo, isibonelo, yokulinganisa isivinini esisheshayo kanye ne:
"Indlela (umzimba) ebingawulandela ukube... ibihanjiswe ngokufanayo ngezinga elifanayo lejubane elivame ukuhanjiswa ngalo ngaleso sikhathi."
Noma kungenzeka ukunquma uhlobo lwendlela embozwe umzimba ongaphansi komfaniswano kanye nokunyakaza okusheshisiwe (njengamanje lokhu kuxazululiwe ngosizo lwezindlela zokuhlanganisa). Leli qembu elifanayo, elakhiwe ngabantu abafana:
- Thomas Bradwardine
- UWilliam Heytesbury
- Richard Swineshead
- UJohn Dumbleton
Impumelelo yabo enkulu wukudala lokho okubizwa I-average Velocity Theorem ukuthi kamuva, kusetshenziswa ulimi lwe-kinematic nolimi olwenziwe lula, yilona oluzofika ukuzobhala isisekelo salokho okwaziwa namuhla ngokuthi "umthetho wemizimba ewayo”, ephakanyiswe ngabakwa UGalileo Galilei.
Enye indoda enkulu okuthiwa Nicholas Oresme okungeye- Inyuvesi yaseParis ngokubambisana nesiNtaliyane Giovanni di Casali, kwakuyibo abayinhloko abahlinzeka ngokuzimele uhlobo lokuboniswa kwesithombe sobudlelwano obalulwe ngenhla. Ngesikhathi kuvuselelwa abeLungu, abaningi babezibuza ukuthi ubani owasungula izibalo, abanye bazi ukuthi owasungula izibalo zazingakaze zibonakale ngaphambili kodwa kwakungama-Arab, amaGibhithe namaGreki ayezisebenzisa kakhulu endulo.
Ikhulu le-XNUMX kuya kwelama-XNUMX
Manje, sizofunda kancane ngomlando wezibalo nokuthi njengoba sesike sachaza, akwaziwa kahle ukuthi ngubani owasungula izibalo, kodwa kuyaziwa ukuthi zavela eqenjini lempucuko eyayisebenzisa isikhathi eside. futhi lokho kwavela phakathi nekhulu le-XNUMX kuya kwelama-XNUMX.
Ukutholwa Kwezibalo Zesimanje
Phakathi nekhulu leshumi nesikhombisa, ulwazi abantu abanalo ngomhlaba kanye nomhlaba wonke lwaqala ukusheshisa futhi ngenxa yalokhu kwakudingeka ukuba kube namathuluzi ezibalo ayengavumela ukuguqulwa kwezinto ezintsha ezitholakalayo ezazizokwenzeka. Kodwa-ke, kwethulwa ibhomu lesibili lesayensi. Ngaleso sikhathi imigomo ye:
- I-Logarithm
- I-Infinitesimal Calculus
- I-Calculus of Probabilities
Futhi nakho konke okwamanje okuhlobene nesisekelo sezibalo zesimanje. Zingaba izinto abantu abaningi ezibonakala zingaqondakali kakhulu, nokho, zingatholakala phansi kwezibalo ukuze zikwazi ukwakha izakhiwo, kanye nokwenza izindiza zindize, ngendlela efanayo ezikhonza ngayo ukuthumela ulwazi ngezindlela ye-inthanethi noma ukuze kuthathwe i-akhawunti yokuthi ungakanani umthamo womuthi okufanele usetshenziswe.
Manje, izibalo ngendlela eqondile azisafundelwa ukusebenza kwazo, kodwa zifundwa ngokuphelele ukuze kuhlolwe izindawo ezingaziwa. Akulona uhlobo lokuzijabulisa olungawenzi umqondo, ngoba ulwazi olutholiwe lukhomba ukuthi yonke intuthuko enkulu eyenziwe kuzibalo iyasebenza ngokushesha empilweni yangempela esiphila kuyo, kungakhathaliseki ukuthi ikude kangakanani futhi ingabonakali. izazi zezibalo zomlando zingavezwa.
Mhlawumbe, ingxenye enkulu yabantu izosala ingenandaba nokuthile engakakwazi ukuthola ukuthi i-hypothesis eyethulwa yindoda ibizwa ngokuthini. U-Riemann ngonyaka we-1859, okumayelana nohlobo lwesiphakamiso sezibalo esingacacile, lapho sikhuluma ngokufihlakala lokhu ngaphandle kwezazi zezibalo.
Kodwa-ke, kungamane kwanele ukwazi ukuthi ikusasa lezokuxhumana lizoncika kakhulu ekubonisweni okunjalo U-Riemann ukuze sikwazi ukwazisa isintu ukuthi izibalo ngaso sonke isikhathi zinohlobo lomphumela oqondile wokuthi buyini ubukhona bempilo yomuntu.
Futhi naphezu kweqiniso lokuthi abantu abaningi bakuthola kunzima ukuqonda konke lokhu, izibalo zisenalo uhlobo lobuhle bangaphakathi, obufana kakhulu nomsebenzi omkhulu wobuciko nezincwadi. Imigomo yobuhle nobuhle icacile kwisayensi yezibalo, futhi mhlazana ukuqaphela lokhu, umkhakha omusha wesipiliyoni uzovulelwa wena.
Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics siyakusiza ukuba uthole ulwazi oluningi kakhulu kunalo onalo, futhi sikumema ukuthi wazi konke ngomlando we-¿Ubani Osungule Injini Ye-Steam? Njengoba lo mlingisi bekumele asebenzise izibalo eziningi ukuze ayidale.
Europa
Izibalo ziza ekuncikeni ezicini zezobuchwepheshe nezomzimba. Indoda eyaziwayo njengoba kwenzeka Isaac Newton futhi of UGottfried Leibniz Yibo abadale i-infinitesimal calculus, okuyisiqalo senkathi yokuhlaziywa kwezibalo ngalezo zikhathi, okuvela ekuhlanganisweni nasekubuyeni kwezibalo ezihlukene.
Lokhu kwenzeke ngenxa yesikhathi esinqunyelwe, esithathwa njengomqondo obaluleke kakhulu ngalesi sikhathi wezibalo. Kodwa-ke, ukwakhiwa okuqondile kwethemu lomkhawulo akuzange kukhiqizwe kuze kube ikhulu leshumi nesishiyagalolunye ngosizo lwe I-Cauchy.
Izwe elikhulu lezibalo lasekuqaleni kwekhulu leshumi nesishiyagalombili lingaphansi kwesibalo somuntu okuthiwa Leonhard Eulerkanye nangeqhaza lakhe elikhulu kuyo yomibili imisebenzi yezibalo kanye nemibono ehlukene yezinombolo, kanti omunye umlingisi oqanjwe igama lakhe Joseph-Louis ILagrange ngumuntu okhanyisa ingxenye yesi-2 yekhulunyaka mayelana nalokhu.
Ikhulu leminyaka elidlule likwazile ukubona ukuqaliswa kwe Ukubala okungenamkhawulo, obekuzovula indlela yokuthuthukiswa okukhulu kwesifundo sezibalo esisha esihlanganisa ukuhlaziya i-algebra, lapho yonke imisebenzi yakudala ye-algebra yengezwa ekuhlukaniseni nasekuhlanganisweni. Ingxenye ebalulekile yomlando wezibalo kanye nokuthi ubani owasungula izibalo eminyakeni yasendulo.
Japan
Izibalo ezithuthukiswa ezifundeni ze Japan phakathi nenkathi Edo phakathi kweminyaka ye-1603 kuya ku-1887, izimele ezibalweni zasentshonalanga.
Ngalesi sikhathi kukhona Seki Kowa, owayengumlingiswa obaluleke kakhulu kulokho okwaba yintuthuko ye wasan okubhekwa njengezibalo ezijwayelekile zaseJapan, futhi okutholwe kuyo ngaphakathi kwezindawo ezifana ne- integral calculus, kuhambisana ngokoqobo nochwepheshe bezibalo abakhulu banamuhla baseYurophu, njengoba kwenzeka komunye obizwa ngokuthi. UGottfried Leibniz.
Izibalo ze Japan kulesi sikhathi esifanayo wabe esegqugquzelwa yizibalo ze China, okuhloswe ngokuyinhloko ezinkingeni zejometri. Kwezinye izinhlobo zamaphilisi enziwe ngokhuni okuthiwa sangaku, ukuthi iziphakamiso zibekwe futhi lokho okubizwa ngokuthi "I-Geometric Enigmas" ixazululwa; kusukela kulelo gama ukuthi livela, isibonelo, owaziwayo i-sextet theorem Soddy.
Sithemba ukuthi uyayijabulela indatshana yethu yokuthi ngubani owasungula izibalo, sikumema futhi ukuthi uvakashele i-athikili yethu Umlando wefoni.
Ikhulu le-XIX
Phakathi naleli khulu leminyaka abaningi babezibuza ukuthi ubani owasungula izibalo futhi iqiniso liwukuthi phakathi nekhulu leshumi nesishiyagalolunye umlando wezibalo ubulokhu uthela kakhulu futhi uchichima. Kuleli khulu leminyaka, kwavela amanani amakhulu emibono emisha futhi umsebenzi owawuqalwe ngaphambili waqedwa.
Kuyinkathi lapho ukuqina kuqala ukubusa, njengoba kuvezwa "Ocwaningweni Lwezibalo" ngophenyo lwe I-Cauchy kanye nesamba sochungechunge, okuyilona elethulwa futhi ngenxa yejiyomethri, kanye neTheory of Functions futhi ngokwesici lokho okubhekisela ezisekelweni zokubala okuhlukile futhi okubalulekile kuze kube yilapho ukwazi ukususa yonke imibono emincane ngokungenakulinganiswa. bakwazile ukuzuza impumelelo ebaluleke kakhulu phakathi nekhulu leminyaka elidlule.
Ikhulu lamashumi amabili
Phakathi nekhulu lama-XNUMX futhi kwakunezinto eziningi ezazingaziwa mayelana nokuthi ubani owasungula izibalo, futhi iqiniso liwukuthi ngesikhathi saleli khulu leminyaka kungabonakala ukuthi izibalo zaba kanjani umsebenzi omkhulu kochwepheshe abaningi nochwepheshe besayensi ababethungatha impendulo umbuzo wokuthi ubani owasungula izibalo?
Unyaka ngamunye, odokotela abaningi bayaphothula, futhi izindawo zokusebenza zitholakala kakhulu kwezokufundisa kanye nezimboni. Amathiyori amathathu amakhulu okubusa aziwa ngokuthi:
- Ithiyori Yokungapheleli Godel.
- Ubufakazi Bokucatshangelwa Taniama–Shimura, okusho ukuthi ubufakazi bokugcina beTheorem kaFermat.
- Ubufakazi Beziqalo ngoba ngenye ingxenye Pierre Deligne.
Inani elikhulu lemikhakha emisha eyakhiwe noma eyazalwa iwuhlobo lokuqhubeka kwayo yonke imisebenzi ye I-Poincare noma iningi labo, futhi mayelana:
- Amathuba
- I-Topology
- I-geometry ehlukile
- Umqondo
- Ijometri ye-algebraic
- imisebenzi ye Grothendieck, phakathi kwabanye abaningi.
Konke lokhu kuvame ukuba yingxenye ebalulekile yesayensi yezibalo futhi ochwepheshe abaningi bavame ukuba nemibuzo ngokuthi ubani owasungula izibalo. Siyethemba ukuthi le ndatshana yokuthi ngubani owasungula izibalo iyakusiza ekufuneni kwakho ulwazi, siyakumema futhi ukuthi uvakashele isihloko sethu mayelana Umlando Wesibonakhulu.
Ikhulu lama-XXI
Ngonyaka ka-2000, isikhungo safona Clay Mathematics Institute Weza ukuzomemezela ukuthi zaziyini izinkinga eziyisi-7 zenkulungwane yeminyaka, kwathi ngonyaka ka-2003 ukubonakaliswa komcabango wendoda ebizwa ngokuthi. I-Poincare eyenziwe ngu Grigori Perelman obengumuntu owacabanga ukuthi angawemukeli umklomelo wale mpumelelo.
Ingxenye enkulu yamamagazini ezibalo anenguqulo ye-inthanethi kanye nenguqulo ephrintiwe, ngendlela efanayo inani elikhulu lokushicilelwe kwedijithali livame ukwethulwa. Kukhona ukukhula okukhulu kulokho okutholakala ku-inthanethi, okuthandwa ngabakwa I-ArXiv. Lolu ulwazi olubalulekile ukuze wazi Ubani Osungule Izibalo.
Umsuka Wezibalo
Ukuze wazi okwengeziwe mayelana nokuthi iyini imvelaphi yezibalo, okokuqala, kufanele ubuyele emuva ezinkulungwaneni zeminyaka ngokuhamba kwesikhathi. Singasho ukuthi namuhla akukho okungeke kwenzeke ngaphandle kokusetshenziswa kwezibalo zezibalo, noma kunjalo, ngaso sonke isikhathi lokhu akuzange kube njalo.
Ekuqaleni kwakuyinto elula. Igama lenombolo laba yinto engenakuphikiswa kakhulu, naphezu kweqiniso lokuthi selivele limele uguquko olukhulu ezingeni lomqondo. Ukukhuluma iqiniso, kukhona idatha ethile esalibele ebonisa ukulandelana kwamamaki okungafanekisela izibalo ezivela eminyakeni engaphezu kuka-30.000 edlule. Futhi ngezibalo yilapho kwethulwa khona imisebenzi ye-arithmetic ebalulekile, okuyilezi:
- Izibalo
- Ukukhipha
Ngalokhu nje, umhlaba omkhulu wamathuba angenamkhawulo wawusuvele uvulekele sonke isintu. Uhwebo lwalungase lusungulwe, amabanga ayengalinganiswa, futhi amabutho nawo ayengase aqhathaniswe namanye.
Kamuva, ukuhlukana nokuphindaphindeka kwaqala ukuvela ngokushesha. Ukusabalalisa izinto nokwengeza amanani kuvame ukuba ezinye zezinto ezivame ukwenziwa nsuku zonke noma ezenziwa ngalezo zikhathi. Kungakhathaliseki ukuthi okwebhizinisi, okomlimi, umthelisi kanye nokuphila kwansuku zonke kwawo wonke umuntu. Lokhu kuyingxenye yendaba ethi Who Invented Mathematics, yona ngokwayo eyayingeyena umuntu oyedwa kodwa yayingabantu ngokwamarekhodi atholakele.
Amagatsha eMathematika
Cishe kuzoqashelwa amagatsha ezibalo angaba ngu-5, ngokuvamile aqoqwe abe yizinkambu zezibalo ezinkulu ezi-4 ezithathwa ngokuthi "Pure", futhi lokhu okulandelayo:
Ubungako: Kulo mkhakha yilapho izinombolo zikhona:
- izinombolo
- Izilinganiso
- Ngokwemvelo
- Izakhiwo
- okunengqondo
Isakhiwo: Ngaphakathi kwalo mkhakha, izinombolo nobudlelwano kusetshenziswa ukuze ukwazi ukubala nokumela amasethi noma izimo ezifana nalezi:
- I-Algebra
- Ithiyori Yezinombolo
- Ama-Combinatorics
- I-Graphic Schema Theory
- Ithiyori Yeqembu
Isikhala: Lapha kulapho izinombolo zilandelana khona ngesilinganiso sesikhala kanye nokubalwa kobudlelwane obungaba khona obuhlukahlukene phakathi kokumelwa kwendawo okuyilokhu:
- I-geometry
- I-Trigonometry
- I-geometry ehlukile
- I-Topology
I-Cambio: Yilapho izinombolo zisebenza khona ukuveza ubudlelwano obushintshayo, ukunyakaza, ukufuduka futhi ekugcineni ushintsho ngokujwayelekile, njengoba kwenzeka ku:
- Ukubalwa
- I-Vector Calculus
- Amasistimu anamandla
- Izibalo ezihlukile
- Ithiyori yesiphithiphithi.
Ingxenye yamagatsha ezibalo yavela kumuntu owasungula izibalo, okungukuthi, isiko lasendulo elalilisebenzisa ngendlela enkulu. Siyethemba ukuthi le ndatshana yokuthi ngubani owasungula izibalo izoba usizo olukhulu kuwe, sikumema ukuthi uvakashele isihloko sethu mayelana Umlando Weselula.
Kungani Izibalo Zibalulekile?
Izibalo yiyona eyenza kube nokwenzeka ukuveza ngokubhala izinombolo kanye nezixhumanisi ezinhle nomhlaba wangempela, futhi yisayensi evula umnyango wazo zonke izindlela ezingabonakali kanye nezibalo eziyinkimbinkimbi kakhulu emhlabeni wonke. Kuyini inqubekelaphambili yabantu, yilokhu okwafika ekucabangeni ukwanda okukhulu kwamandla okukhipha kanye nokukwazi ukuphatha imibono eyinkimbinkimbi.
Nokho, phakathi nomkhakha wocwaningo owabonakala ungenalutho futhi uhlukanisiwe nalokho okuyikho ngempela ukuphila, intuthuko enkulu iye yahlukaniswa nayo nezinye izigaba zesayensi, kokubili ezobuchwepheshe nezimboni, njengoba Ngaphandle kwalokho, bebeyontula uhlobo oluthile lwesayensi ehlelekile. ulimi ukuze lukwazi ukuveza imisebenzi yezibalo. Lokhu kubalulekile ngoba noma ngubani owasungula izibalo wayazi kancane ngokubaluleka kwazo.
Yenzelweni iMathematics?
Izibalo zisetshenziswa nsuku zonke ukwenza izinhlobo ezahlukene zezilinganiso. Izibalo ziwuhlobo lwethuluzi lengqondo elinamandla kakhulu. Izibalo zivumela umuntu ukuthi akwazi ukwenza uchungechunge olukhulu noluyinkimbinkimbi lwemisebenzi enolunye ekuphileni kwansuku zonke, njengoba kwenzeka:
- Incazelo kanye Nokuhlaziywa Kwezikhala
- Ubudlelwano
- Ubuningi
- Qalisa
- Izilinganiso
- Ukuqiniseka
Ngaphandle kwanoma yikuphi kwalokhu, akunakwenzeka ukuba ukwazi ukubala, ukwazi ukulinganisa, noma ukukwazi ukunquma ngokunengqondo izinto ezibonakala nsuku zonke ekuphileni kwabo, ngakho bazisebenzisa ngaphandle kokucabanga ukuthi basebenzisa izisekelo eziyisisekelo. isigaba sesayensi esidala ngempela. Konke lokhu kungenxa yokubonga kunoma ngubani owasungula izibalo.
Izicelo Zezibalo
Ngaphandle komkhakha wezibalo othi “Pure” noma osemthethweni ngokuphelele, kunezinhlobo ezithile zezindawo lapho izibalo zinikezelwa khona ukuze kufundwe izici zeminye imikhakha yolwazi, ikakhulukazi leyo okuhloswe ngayo ukwakhiwa kwamathuluzi ocwaningo nokuxazulula izinkinga. zezinkinga zezibalo. Ezinye zalezi zindawo zokusetshenziswa kwezibalo yilezi:
Izibalo
Lezi izibalo ezivame ukusetshenziswa emathubeni kanye nasemakhonweni okubikezela izehlakalo ngezinga elilinganayo noma lephesenti, ukuze ukwazi ukwenza izinqumo ezifanele nezihlosiwe.
Amamodeli Wezibalo
Yilezo ezisetshenziselwa ukumelwa kwezinombolo njengendlela yokulingisa izici zeqiniso lansuku zonke, ukuze sizame ukubikezela noma ukuqonda ngokufingqiwe ubudlelwano obukhona kuzo. Kuzuzisa ngokukhethekile ukuthi iyini indawo yekhompyutha.
Izibalo Zezezimali
Kulokhu zisetshenziswa emhlabeni jikelele wezezimali, njengoba izibalo kulokhu zivame ukuboleka uhlobo lwayo lolimi oluhlelekile ukuze kuboniswe kokubili ubudlelwano bezentengiselwano nezomnotho okuyibo okuyibo abakha lo mkhakha obaluleke kakhulu emphakathini wamanje nowakudala njengoba kahle..
I-Mathematics Chemistry
Isayensi yekhemistri iyona esebenzisa izibalo ukuze ikwazi ukuveza ubudlelwano bengxenye evame ukwenziwa ngezindlela ezihlukahlukene nezingenzeka zokusabela kodaba olushiwo.
Izinhlobo Zokusebenza
Ngokusho I-Chevalard, a Bosch futhi ukuze i-gascon, uphethe ngokuthi bekukhona cishe izinhlobo ezi-3 zokuhlinza ezingenziwa ngezibalo:
Sebenzisa Izibalo Ezaziwa
Lokhu kuhlanganisa ukuthatha izinqubo ezidalwe ngabanye abantu futhi bazenze ezinkingeni zabo ukuze zikwazi ukuxazululeka, kuphela ukusebenzisa ingqondo eqoqiwe nolwazi lwezinombolo njengethuluzi.
Bafunde Futhi Bafundise
Lapho kukhona inkinga enzima, umuntu angaphendukela kochwepheshe bezibalo abakhulu kunabo bonke noma kwezinye zezincwadi zayo, ukuze akwazi ukufunda ukuphatha zonke izindlela ezingaziwa kuze kube manje futhi ngaleyo ndlela andise eyabo indawo yokugcina. babe.
Dala Izibalo Ezintsha
Esimeni esinjalo lapho lingekho ithuluzi lezibalo elibasebenzelayo ukuxazulula inkinga ethile, umuntu angaqhubekela ekudaleni eyodwa, inqobo nje uma kuthatha njengesiqalo lezo esezivele zaziwa kuze kube yimanje.
Ochwepheshe bezibalo abadumile
Emlandweni wezibalo kuneqeqebana labantu abebethathwa njengezazi zezibalo ezidume kakhulu emhlabeni wonke kusukela emandulo kuze kube yimanje. Yiqiniso, akekho kubo owasungula izibalo. Phakathi kwazo kukhona okulandelayo:
- UPythagoras waseSamos kusukela ngonyaka wama-570 - 495 ngaphambili UKristu.
- Euclids yonyaka wama-325 - 265 ngaphambili UKristu.
- ULeonardo Pisano Bigollo kusukela ngonyaka we-1170 - 1250.
- URené Descartes kusukela ngonyaka we-1596 - 1650.
- Leonhard Euler kusukela ngonyaka we-1707 - 1783.
- Andrew Wiles kusuka ngonyaka we-1953
Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics sibe nesithakazelo esikhulu kuwe nokuthi kungenzeka ukuthi uthole ulwazi oludingekayo ngomlando wayo, imvelaphi, lokho ezisetshenziselwa kona futhi ikakhulukazi owasungula izibalo.


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Isekelwe e-Fuzhou / China, inkampani yethu ikhiqiza izinhlobo eziningi zemikhiqizo Yezingubo zangaphandle kanye Nezingubo Zokusebenza: Amabhantshi, Ama-Softshell, Ama-Bodywarmers, Ama-Polar Fleeces, Ama-raincoat, I-Windbreaker, Ukubonakala Okuphezulu, Amabhulukwe, Amaphinifa, njll.
Ukuhlanganisa isipiliyoni kanye nolwazi ekukhiqizeni izingubo eziyinkimbinkimbi ehlukahlukene, imboni yethu ikhethekile ekukhiqizeni izingubo zokusebenza ezenziwe ngokwezifiso, imifaniswano, izingubo zangaphandle kanye nezingubo zemvula ngenxa yokuguquguquka kwayo okubalulekile nokusebenza kabusha kwekhwalithi ephezulu eyenziwe ngokwezifiso ukukhiqizwa. Sinezindawo zokukhiqiza ze-7000 m2 ezinemishini ezenzakalelayo ngokuphelele futhi uhlelo lokugcina. Umthamo wethu wokukhiqiza ungama-600,000 izingcezu ngonyaka.
Ukusebenza kwekhwalithi engashintshi ye-Trustop nesevisi kuvame ukudlula lokho okulindelwe amakhasimende ethu.
Singakunikeza ikhwalithi engcono nezingubo zokuncintisana.
Sinomugqa ophelele wokukhiqiza kanye nesipiliyoni esicebile konke ukugeleza kokukhiqiza, kungasindisa ngempumelelo izindleko zezinto kanye nokulawulwa kahle kwekhwalithi. Ngokuthuthuka kweminyaka, ukubambisana okuhle nobudlelwano bokunqoba-wina nabahlinzeki bezinto abahlukahlukene kungaqinisekisa ukuthi sithola impahla ngesikhathi futhi sithole amanani angcono. Sinolwazi lochwepheshe lwezingubo zokugqoka, singakunikeza iseluleko lapho ukhetha impahla noma izesekeli, kungasindisa isikhathi sakho futhi kwandise inzuzo yokuthengisa.
IZIDINGO ZAKHO, IZIMALI ZETHU
Themba
Senza ucwaningo lokuthi kungenzeka yini ngaphambi kwanoma iyiphi iphrojekthi entsha. Sikugcina ukwaziswa ngaso sonke isikhathi mayelana nenqubekelaphambili yokukhiqiza, futhi sigcina kahle kakhulu ukubonwa kweminqamulajuqu.
Ukuncintisana
Kuwo wonke amaphrojekthi silazi kahle iqiniso lemakethe, yingakho sinikeza amanani ancintisanayo futhi siqinile ngemuva kokugunyazwa kwe-oda. Singakusiza ngemininingwane yobuchwepheshe yephrojekthi yakho (izindwangu, uhlobo lokwenza ngendlela oyifisayo...) ukuze uvumelanise ukunikezwa kwethu nokuma komkhiqizo.
Ikhwalithi
Kusukela ezintweni ezingavuthiwe (izindwangu eziqinisekisiwe ze-Oeko-Tex, izintambo ezifekethisiweyo ze-Madeira, njll) kuya kunqubo yokuthunga ngendlela yamasu okufaka uphawu, siqikelela ukuthi isinyathelo ngasinye sokukhiqiza sihlangabezana nenqubo engcono kakhulu yekhwalithi.

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Lesi siphathi sekhadi le-Ca-Mei elincanyana nelikhanyayo lalabo abafuna ukwenza kahle amaphakethe abo.Ngocwaningo lwethu, phatha kalula futhi ukhokhe kalula uba yimfashini, ukheshi akusadumile njengakuqala, umnikazi wamathikithi wendabuko omkhulu ephaketheni lakho akasafanele ukuphila kwethu kwanamuhla.Ngakho sithola izindlela ezingcono zokuphatha nokuvikela izithombe zakho, amakhadi kanye nemali.Abaklami be-Ca-Mei bafaka umbono wabo wokusungula impilo kulesi sikhwama, sithuthukiselwe ukwanelisa abantu abafuna ukuphatha ukheshi namakhadi abo kalula, inhloso yethu yokwenza impilo ibe ngcono.
Ikhwalithi ye-Premium- I-Minimalist slim wallet dimension: 145*115 MM, umumo wonxande.Yenziwe ngezinto ze-PVC eziqinile, ezingagugi zinikeza isivikelo esihle othulini, imihuzuko namaqhubu.Ukuthungwa okuqinisiwe kuthuthukisa ukuqina kwesikhwama samathikithi.
Idizayini eyisitayela- Idizayini yokugoqa yakudala.Umsebenzi omuhle kakhulu nomklamo ongokoqobo, ohlangene, uyaphatheka, isisindo esilula nokho mncane.
Igumbi eliningi -Lesi siphathi sekhadi sinezikhala ezi-2amagumbi, ingabamba amakhadi angafika kwayi-10.2 izikhala zewindi eziseceleni ezicacile ze-albhamu yesithombe, i-ID, ibheji lomsebenzi noma ilayisense yokushayela, izikweletu zemali zansuku zonke, izinhlamvu zemali, amathikithi, amarisidi, amakhuphoni, amanothi, amakhadi ebhizinisi, amakhadi obulungu, amakhadi esitimela, amakhadi esikweletu, amakhadi edebhithi, amakhadi asebhange, iphasiphothi amakhadi, njll.
Imibala ehlukahlukene- Sinemibala engu-4 ehlukene ongakhetha kuyo (ehlukahlukene, noma ebomvu, ephuzi, empunga, emnyama) ngakho-ke hamba, khetha intandokazi yakho futhi uphathe umhlaba wakho ngobumnandi obuphilayo!
Unisex- Uma kubhekwa idizayini yayo eshelelayo kanye nokwakhiwa kwesikhumba okushelelayo, le mikhono idumile ngokubamba amakhadi amancanyana kwabesifazane nabesilisa.Benza imibono emihle yezipho kubahambi empilweni yakho!Ilungele abantu bayo yonke iminyaka.
Inqubo yezobuchwepheshe- Ipuleti lokuhlola ngaphambi kokubeletha–Ukusika impahla–Ukukhishwa kwempahla–Ukuthunga–Ukupakisha
Ikhwalithi yokulawula- Hlola izinto zokwakha&ufanelekile- Ishabhu QC isheke- Isheke lomhloli wokukhiqiza- Isheke lomphathi eliqedile- Isheke lomphathi we-Warehouse- Isheke le-AQL


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Impela uke wacabanga ukuthi kuzoba khona yini okungathuthukisa amakhono akho, okuzokwenza ukuthi, uma wenza…
Umgomo wokuya enyuvesi uyingxenye yohlelo lwekusasa lomsebenzi wabafundi abaningi. Kuyigoli...
Umhlaba wokushicilela ubhekene nenkathi yokukhula namuhla. Izincwadi ezibhalwe ngababhali abawine izindondo nababhali abadumile zithola…
Indlela yokwenza i-resume ngegama ukuze ufune umsebenzi? I-resume idokhumenti yochwepheshe esebenza ngamandla….
Udokotela Wamazinyo: kuyini nokuthi yiziphi izinzuzo ezinikezayo. Thola ngezansi! Ukunakekelwa kwezempilo kwamazinyo kuhambisana nezinhlobonhlobo…
Isifiso solwazi, uthando lokufunda kanye nelukuluku yizithako ezingondliwa…
Ucwaningo luthola imibono eyahlukene kuye ngohlobo lomsebenzi. Uma umfundi engena kusilabhasi ...
I-confectionery ibamba iqhaza elikhethekile ngesikhathi sokugubha uKhisimusi. Isikhathi sonyaka lapho...
Ungawenza kanjani umbhalo ophikisanayo? Ukufunda ngokuqondisisa kubalulekile ukuze ujule mayelana nencazelo yesihloko esithuthukisiwe ...
Ithiyetha isiyalo esinomthelela obalulekile emphakathini. Esikhathini sakamuva, uhlangabezane nesikhathi...
Umsebenzi we-actress ungenye yezinto ezithandwa kakhulu. Kodwa-ke, kungenzeka futhi ukuthi umuntu abone ukuthi ...


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Uma uke wakha ucwaningo futhi unethemba lokuthola okutholakale kokulinganisa nobungako kuzimpendulo, uyaqonda ukuthi kunzima kangakanani ukubuza imibuzo. I-verbiage, ukwakheka nohlelo lolimi olucelayo kungaholela emiphumeleni ezoholela ekucwaningweni kocwaningo lwakho.
Njengomphathi womkhiqizo, ngagijimela kulokhu okuningi ngamaqembu wokugxila. Ukube bengivivinya i-interface entsha yomsebenzisi, ukucela impendulo kungenza umamukeli ahlole isikhombimsebenzisi ukuze azame ukuthola okuthile okungahambi kahle… yize kungenzeka ukuthi yakhelwe kahle. Uma ngibuza ukuthi kukhona yini okunzima noma uma kukhona okushodayo, umsebenzisi angabheka ngokushesha inkinga… okungenzeka ukuthi ayikho.
Esikhundleni salokho, simane sacela umsebenzisi ukuthi athathe isenzo abese echaza ukuthi bahamba kanjani ngesenzo. Ngenkathi lokhu kususa noma yikuphi ukuchema, kudinga ukuhlaziywa okuningi kokuthunyelwe ukulinganisa imiphumela ekucabangeni kwekhwalithi noma ezincomweni. Leyo miphumela bekuvame ukuthi kube njalo ukuqagela okuhle… Hhayi i isiphetho esivumelekile ngokwezibalo.
Ukucubungula Kanjani Ulimi Lwemvelo Nokufunda Komshini
Eminye yemininingwane ecebe kakhulu, eletha uguquko evela ngokucela imibuzo evulekile. Kungani uyisibonelo esihle. Kepha impendulo ku kungani akuyona impendulo yezinombolo, kanambambili, noma yokukhetha… ngakho-ke bekulokhu kunzima ukuthola imiphumela yobungako nekhwalithi oyidingayo ngokubuza imibuzo evulekile ukuqondisa izinqumo zebhizinisi.
Ngokujabulisayo, ukucutshungulwa kwezilimi zemvelo (NLP) kanye ne- ukufunda imishini (ML) ingazinqoba lezi zinkinga! Ngokuhlanganisa ukufunda komshini nobuhlakani besixuku, I-GroupSolver iyipulatifomu yezobuchwepheshe bokucwaninga emakethe esebenzisa ubuhlakani bokufakelwa ukubuza nokuhlanganisa imibuzo esezingeni eliphakeme kanye nemibuzo eningi ekuhloleni okuku-inthanethi.
Ukubuka konke kweGroupSolver
I-GroupSolver ingena phakathi kwamapulatifomu ozenzela wona, njengeSurvey Monkey neGoogle Surveys, nezinkampani zocwaningo ezigcwele, njengeMcKinsey & Company neAccenture.
Okwenza iGroupSolver ihlukaniswe yindlela yabo yokucubungula izimpendulo zolimi lwemvelo, besebenzisa:
- Isixuku Intelligence - Abaphenduli baphendula imibuzo evulekile ngamazwi abo, bese bayasebenzisana.
- Ukufunda komshini - Izimpendulo ezivela emibuzweni evulekile zicutshungulwa nge-algorithm enamandla futhi yokuzilinganisela.
- Izibalo Ezithuthukile - ipulatifomu iqinisekisa izimpendulo zolimi lwemvelo futhi ilinganise imininingwane esezingeni elifanele.
Amathuluzi weGroupSolver Afaka
- I-AI Open Answers ™ - Ngokuhlanganisa ukufunda komshini nobuhlakani besixuku, iGroupSolver ihlela ngokuzenzakalela futhi ilinganise izimpendulo ezivulekile. Akukho ukuqeqeshwa kwedatha, akukho ukulinganiswa komuntu, futhi akukho ukufaka amakhodi kwamahhala okudingekayo.
- IdeaCluster ™ - I-IdeaCluster ikhombisa ukuhlangana phakathi kwezimpendulo ezingaphenduliwe. Kusiza kakhulu lapho kwakhiwa amakhasimende we-personas noma uxoxa indaba yomkhiqizo. Lokho kulungile - amamodeli wokuhlanganisa akhululiwe weGroupSolver nobukhulu obuvela ebudlelwaneni obukhethekile nedatha yokulinganisa.
- IntelliSegment ™ - I-IntelliSegment iyithuluzi lokuhlukanisa elinobuhlakani elingakusiza uqonde ukuthi izimpendulo zemibuzo evulekile zihluka kanjani kumasegmenti athile ophendulayo. Kufana nokuthola indaba esitokisini.
- IdeaCloud ™ - I-IdeaCloud isethulo esihlanganisiwe nesibekwe eqhulwini sezimpendulo ezisekelwa kakhulu embuzweni ovulekile. Ifonti enkulu isho izimpendulo ngokusekelwa okuphezulu phakathi kwabaphendulile. Ifonti encane ngeyokuthi… kahle, izimpendulo ezingazange zikwenze kahle.
- Isixazululo Sokuvumelana ™ - Isixazululo Sokuvumelana yisethi yezimpendulo ezisekelwa kakhulu ezihlobene ngokuqinisekile. Kukhombisa izimpendulo ezihambisana kahle futhi ezakha isivumelwano sokuvumelana phakathi kwabaphendulayo.
- Kuphendula uKhetho - Ngaphandle kokuba yisinkwa nebhotela yocwaningo lwenhlolovo, izimpendulo zemibuzo ekhethwa ngabaningi zingasiza ekwakheni izingxenye eziphendulayo zemininingwane ecebile. Sizigcina zintsha futhi zivuselelwa ngesikhathi sangempela.
- Umngenisi wedatha - Uma usuvele uqoqe imininingwane mayelana nabaphendulayo, ungayilayisha kudeshibhodi yethu. Yisebenzise ukusika idatha yeGroupSolver noma ukwakha izingxenye ezintsha zabaphendulayo.
- Umphathi Wezimpendulo - Buka ukuthi abaphenduli bayiphendula kanjani imibuzo yakho ngesikhathi sangempela. Qoqa bese uwaqinisekisa ngokuchofoza inkinobho. Siyawethemba umshini wethu, kepha imininingwane kwesinye isikhathi idinga ukuthintwa okuthambile komuntu.
- Isilandi sedatha - Thumela idatha eluhlaza ukuze uhlaziye ngokuqhubekayo ngesoftware yezibalo ejwayelekile njenge-SPSS, R, noma i-Excel.
Ideshibhodi ebonakalayo yeGroupSolver inika amandla abasebenzisi ukuthi babuke futhi basebenze ngokuqonda kwakho. Idatha icutshungulwa futhi ibuyekezwe njengoba iqoqwa, ukuze ukwazi ukuhlola kuqala imiphumela nganoma yisiphi isikhathi.


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Ngaphandle kokungabaza, imaski yobuso ibambe iqhaza elikhulu ekulweni kwethu ne-COVID-19.NgoJanuwari, lapho isimo sisibi, abantu kulo lonke elaseChina baqala ukugqoka imaski ubusuku bonke.Lokho, kuhlangene nezinye izindlela, kusize ukumisa i-COVID-19 ukuthi iqhubeke nokusabalala.
Isizathu esisodwa esenza wonke umuntu agxile kumamaski ukuthi ayasebenza, futhi indlela elula yokuqinisekisa ukuthi ukuvikela ukusabalala kwegciwane.
lapho uvakashela izindawo zomphakathi eziminyene njengamabhasi noma amakheshi, lapho umuntu egula, noma lapho evakashele ezibhedlela, abantu kufanele bagqoke imaski yobuso.Ngakolunye uhlangothi, ukugeza izandla njalo, ukufaka amagciwane izinto zansuku zonke ngemva kokuthinta, nokugcina ukusondelana nomphakathi kuyihawu elihle lokubhebhetheka kwalolu bhubhane.
Isikhathi sokuthumela: May-20-2020


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Izindaba
UGwala uyaziphendulela odabeni lomhlaba
nguMNU uBLESSED GWALA
Kukhona umuntu ozibiza ngoBuyekhaya Ndwandwe waseMeveni uthi ungumzukulu kaSvathuza obhale ephepheni lakho iBayede lamhlaka 5 -12 kuMbasa ekhasini lesishiyagalombili (8) ngaphansi kwesihloko esithi “Umlando wamapulazi aseNgoje uvusa iminjunju”
Kwaze kwanzima emhlabeni nxa sekunabantu abasenga ezimithiyo njengomzukulu kaSvathuza. Unekhono lokwakha udaba aze aluvunulise kahle ukuze kungene imfundisoze emqondweni yabantu. Into ehlupha kakhulu ngamanga ukuthi awagcini nje ngokuba nemicondo kodwa anobhatomu bemilenzanyana ezigqunswana.
Okokuqala nje udaba lomhlaba lusematheni kimina selokhu ngaqala ukuba umholi. Ngesikhathi uMntwana wakwaPhindangene iNkosi yakwaButhelezi elwelwa umhlaba waseNgwavuma ukuba unganikelelwa eSwazini ngangikhona nakuba ngangingakangeni eSishayamthetho.
Udaba lwakaSokhulu nolwaseDukuduku oluthinta umhlaba ubolubuza kimina saze saya enkantolo yezomthetho. Udaba lwaseNgoje ngilwazi silusebenza neNkosi uMntwana wakaNgenetsheni ebhekene nabamhlophe abathatha umhlaba wakwabo. Ngingabala ngifikephi bakithi?
Sengiyilungu leSishayamthetho kuHulumeni waKwaZulu ngangiyingxenye nesishabasheki sokweseka ubuhlakani boMntwana waKwaPhindangene ukuba kusungulwe uhlaka olubizwa nge-Ingonyama Trust ukuvikela amanenjana omhlaba asala ngenkathi imibuso yamaKoloni kanye nobandlululo bezidikadikela nje umhlaba wokhokho bethu. Waphasa lowo mthetho ukuze umhlaba weSILO naMakhosi, nabantu bawo ungadliwa njengemali yamadayisi.
Uma ungaya ePhalamende ufunde izinkulumo eziqoshiwe phansi ungazizwela ukuthi ngithini ngodaba lomhlaba kanye nendlela okuphethwe ngayo abantu basemapulazini. Ngingethande neze ukuba umfo kaNdwandwe akhulume imfeketho ngami ukuze agqame emhlabeni. Angizufundiswa nguye uNdwandwe ilanga seliyoshona ukuthi ngikhulume kanjani nokuthi ngikhulume ngani.
Akufanele uMnumzane uNdwandwe angigudle ngokuba angakhele imingcele, angibekele nemigoqo, ezweni leNgonyama; angibize ngomuntu waseShowe oze wawela iMfolozi ebheke eNgoje. Angiyena umuntu wokufika lapha eZululand, mhlawumbe abakuchazelanga laba abakudukisayo.
Mina ngingumzukulu kaKhilane; ulele laphaya kwaGwabhela ngaseNhlophenkulu kwaNongoma. Eminye imizi yakhe iseNdliwayini, hhayi eNdlangubo. Kanti ngasohlangothini lwasekhaya komama ngingumzukulu kaZibezwile kaZembe kaMhlekehleke laphaya Osuthu. Umnewabo kaZibezwile omdala uLokothwayo (Injuq’edl’amahleza!) ilele kwaThengisangaye (eMiddelburg) owaweyinceku yeSilo sasoSuthu uDinuzulu kaCetshwayo, owahlupheka neNgonyama ihlukunyezwa ngabamhlophe. Yena uLokothwayo noZazini uMkhulu, amathambo abo alele ezintabeni bengakaze babe nokuthokoza empilweni ngenxa yempatho yombuso wobandlululo.
Empeleni okushiwo uMnumzane uNdwandwe yikho okuvusa iminjunju kimi nxa engangithatha njengeyethangana eleseka amaBhunu. Kwamina nginezibazi zabamhlophe bebopha izinkomo zami ezinye zigcine seziyiswa esikiti lena eBabanango, kwesinye isikhathi zibuye zingasaphelele ngezindlela eziningi; enye yagcina ishaywe inyoka; angikaze ngikhokhelwe nanamhlanje. Kungabe yimi engeseka izenzo ezingenabo ubulungiswa yini na? Ngicela uMnumzane uNdwandwe anake izinkinga zakhe, ayeke ukubhekana nami.
Okwesibili, njengoba ngishilo, amanga ayashesha ukuhwamuka njengenkungu; kanti andiza ebusuku njengelulwane elesaba ukundiza emini ngoba lesaba izinyoni ukuthi zizolibuza ngale nkahlankahla yetende lamaphiko elindiza nayo.
Ngibe yiMeya yesifunda saseZululand kusukela mhlaka zingama-20 kuNhlaba wezi-2010, ngasebenza izinyanga eziyishumi nanye kuphela, ngoba ngangena vele sekuyophela ihlandla lalowo owayeyiMeya. Ngale sosikhathi uMnu uThemba Khoza othi uNdwandwe ngangihamba naye, kwasekuphele iminyaka engaphezu kweshumi adlula emhlabeni, njengoba ahamba ngoNhlaba we-1999. Kusho ukuthi umbhemi lona ufuna abantu bakholwe ukuthi mina ngaya eNgoje ngiphelekezelwa umufi uThemba Khoza? Ngisho angazama ukuguqula inkulumo athi lokhu akushoyo kwenzeka phambilini kuka-1999 kwakungeke vele iPhini likaNgqongqoshe Wezemisebenzi kuZwelonke, noma uNgqongqoshe Wezemfundo KwaZulu-Natal, uMhlonishwa u-Eileen KaNkosi-Shandu, ethule ilungu nje phaqa leSishayamthetho libe isukhulumi sosuku. Amanga aluhlaza, okungathi noma ungalanda amalahle akwaMnyathi uzama ukuwapheka, angevuthwe!
OkaNkosi Shandu ulisebenzele izwe lakithi, futhi uyabazi ubunzima bempilo yasemapulazini, njengoba akhulela KwaBanakile khona eNgoje. Ngakho, ngeke aba uhlobo lomuntu ochazwa uNdwandwe namhlanje. Ngeke ngivume uNdwandwe achikachike umdondoshiya weqhawekazi lakithi elifana noKaNkosi Shandu, ahudulelwe phansi, ngokuthi wathi abantu abancethezele abeLungu.
Ngeke samvikela uMnu uHenry Combrinck (“uTsotsi”) uma kukhona okubi akwenzayo, kodwa akekho owake wammangalela eqenjini le-IFP, noma kimina njengoba uNdwandwe engethwesa icala nje. Uma kwakukhona okubi akwenza, sasingeke simvune njenge-IFP. Kwayona inhlangano ayibiza ngeRAFOSA, ayikaze ingithinte ngalezi zinto, ngakho ke, bengingeke ngibhule ngingeyiso isangoma.
Udaba lomhlaba noBukhosi lubucayi njengenhlamvu yeso, aludingi ukukhulunywa budlabha njengoba uMnumzane uNdwandwe ekhuluma. AbaseZimbabwe, balushovuza kanje kodwa nanamhlanje kusekhona izinkinga ezinkulu kwaze kwazika nomnotho wezwe. Ngakho, uMnu uNdwandwe angathi ngiphumaphi manje, nokuthi ngikhuluma ngoba selukhulunywa amaqembu aphikisayo udaba lomhlaba. Athini aphikisayo Ndwandwe? Asho lokhu okwakushiwo eZimbabwe? Nawe ukholwa yikho? Klibhi klolo lingcono iklolo ngoba liyadliwa.
UMntwana wakwaPhindangene, wayeze ethi akungenelele amazwe omhlaba (International Mediation) njengoba enobuchule obujulileyo bokuthi udaba loBukhosi nomhlaba aludingi ukuthathwa ngesinxele; nokuthi ludinga abalukhulumayo babeqotho, kwabakushoyo. Futhi, bangaphathi ngodaka emehlweni abantu. Ngeshwa, iqembu elibusayo lashaya ingwijikhwebu emveni kokhetho lomhla zingama-27 kuMbasa we-1994 kuze kube manje; udaba alukaxazululeki. Angazi ulindeleni kulawo maqembu othi azalwe izolo. Kanti wena Ndwandwe, unele uzwe umuntu ebhula ihawu ungamazi bese umbongela njengeqhawe, uthi uyingqwele uqala nokumbona, ungakaze uzwe nokuthi wake washaya muphi ungcede phambilini. Cha usenkingeni mfo kaMvathuza!
IQembu leNkatha yeNkululeko liyohlala liyithemba labantu, ngoba liyabakhuthalela, futhi liba nabo ngezikhathi ezinhle nezimbi; noma behlukunyezwa, nanoma ngubani noma ngaluphi uhlobo. Kodwa alikaze lilinge ukuba liqhube impi yobuhlanga nokucwasa abanye abantu ngobuzwe babo; ngenkolo yabo, nolimi, noma ngamasiko abo kumbe ukuhambisa inzondo phambili. uMnu uNdwandwe akalwe impi yakhe yobuhlanga nenzondo angafaki amagama abantu nabaholi. Ayi mfo kaNdwandwe, uyakwazi ukusikela umuntu ibheshu ulithunge ngendlela elizomfanela ngayo. Abakukhuze uzokwedlula!
- Ikhishwe: uMnu uBlessed Gwala, MPL, uSihlalo KaZwelonkwe eQenjini leNkatha


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Isignali ye-HDMI enwetshiwe kowesilisa kuya kowesilisa 24AWG isekela ukulungiswa kwe-HD 4K/2K
Imininingwane Yomkhiqizo
Omaka bomkhiqizo
Ukucaciswa Komkhiqizo
Imininingwane Yomkhiqizo
* Ukusekelwa okude kakhulu okungu-30M (ubude obuthile buncike ekucacisweni kwentambo)
* Sebenzisa ikhebula elijwayelekile lenguqulo ye-AWG24 HDMI 1.4, isekela i-CEC, ehambisana ne-HDCP;
Izici Zomkhiqizo
Ikhebula le-4K HDMI Ixhuma Itiyetha Yasekhaya noma Izingxenye Zomsindo Wezimpawu Zedijithali
Le ntambo ye-HDMI enesivinini esikhulu ixhuma ngokuvikelekile ama-Chromebook, ama-MacBook, amaphilisi, ama-PC, izidlali ze-Blu-ray, ama-game consoles, amabhokisi e-Roku/Apple TV noma izamukeli ze-TV zesathelayithi/ikhebula kuma-HDTV, amamonitha e-HD, amaphrojekhtha noma izamukeli zetiyetha yasekhaya.Ikuvumela ukuthi unwebe isignali yakho ye-HDMI ifike kumamitha angu-30 ukusuka emthonjeni ngaphandle kokuxhuma isiginali ye-booster noma ukusebenzisa intambo ebiza kakhulu esebenzayo (AOC) noma intambo ye-Cat5/6.Iphinde isekele i-Ethernet, ngakho-ke ayikho ikhebula ehlukile edingekayo ukuze kuxhunywe amadivayisi ku-inthanethi.
Jabulela Ukucaca Kwevidiyo Ye-4K HDMI Ngomsindo Weziteshi Eziningi
Le ntambo ye-Tripp Lite 4K HDMI ihlinzeka ngoxhumo oluhlanzekile lwedijithali olusekela ukulungiswa kwevidiyo ye-Ultra HD kufika ku-4096 x 2160 (4K x 2K) ngo-30 Hz ngesithombe nomsindo ocace bha.
Tshala Ekwakhiweni Kwekhwalithi Ukuze Kusebenze Okunokwethenjelwa
Izinto zekhwalithi ephezulu ziqinisekisa ukusebenza okuvelele kukho konke ukuphila kwekhebula lama-24 AWG.Othintwayo nezixhumi zifakwe ngegolide ukuze zimelane nokugqwala.Ukuvikela kabili kunciphisa umsindo womugqa (EMI/RFI) ongaphazamisa amasignali ahamba ngentambo ye-HDMI.Uma isetshenziswa ne-adaptha yedijithali ye-Apple A/V, ikhebuli isekela isibuko sevidiyo se-iPad2 ukuze udlale imidlalo, ubukele amavidiyo noma ubonise izethulo.
Ikhebula le-30M likuvumela ukuthi udizayine uhlelo lokusebenza lomsindo/lwevidiyo emincamweni yakho
Le ntambo ende ye-HDMI ikuvumela ukuba ube namandla amakhulu ekubekeni ithiyetha yakho yasekhaya noma izingxenye zezimpawu zedijithali.Isibonelo, isidlali sakho se-Blu-ray noma iseva yemidiya ingase ifihleke kude nesibonisi esixhunyiwe ngezinjongo zokuphepha.
Izicelo Ezijwayelekile
Buka ividiyo ye-4K kusuka kusidlali se-Blu-ray, ikhonsoli yegeyimu, ikhompuyutha ephathekayo noma ithebhulethi kumabonakude we-Ultra HD, imonitha noma iphrojekhtha
Xhuma i-Chromebook noma i-MacBook ebhokisini le-A/V letafula lenkomfa ukuze unikeze isethulo sevidiyo esikrinini esikhulu.
Dlala ku-inthanethi noma imidlalo yevidiyo ye-PC ebonisa izithombe ezifanele
Hlanganisa ne-adaptha yedijithali ye-Apple A/V ukuze usekele isibuko sevidiyo se-iPad2
Thumela okuqukethwe kwevidiyo kwe-4K kuzimpawu zedijithali noma izibonisi zendawo yokuthengisa
Isicelo
Amadivayisi okokufaka: Imithombo yesignali ene-HDMI esibonakalayo esikhiphayo, njengamakhompuyutha, i-PS3, amabhokisi e-HD set-top, amakhompyutha we-Apple, ama-MacBooks, amabhuku okubhalela we-Xiaomi/Huawei/Lenovo/Samsung/Dell nezinye izinto zokusebenza.
Amadivayisi wokubonisa: Bonisa amadivayisi ane-HDMI okokufaka, njengamathelevishini anencazelo ephezulu, amamonitha anencazelo ephezulu, namaphrojektha.


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Amakhosikazi lana ayosinisa angena emzini kuhwelela, afike alungise isikhundla nokudla okuyofike kudliwe umntwana. Umkhongi yena uhamba kancane ehamba ejeqeza emuva efuna ukuba neqiniso lokuthi ngempela udwendwe luyamlandela, phela akwaziwa.
Lolu daba luyatholakala njengamanje kuBAYEDE ONLINE kuphela kulabo abane-akhawunti (subscription).
Uma une-akhawunti, sicela uqhafaze lapha.
Uma ufisa ukuvula i-akhawunti, uthole konke okwethulelwa iBAYEDE ONLINE, qhafaza lapha.
Uma unenkinga noma umbuzo ungasithumela umlayezo ku subscriptions@bayedenews.com, noma ungashaya ucingo emahhovisi eBAYEDE ku 031 765 6662 noma 031 765 3302 ngezikhathi zomsebenzi.


text:
Kusuka ocwaningweni nasekuthuthukisweni kuya ekuklanyweni kuya ekukhiqizeni, ngemuva kwezinsuku ezingama-40 zemizamo yabo bonke abasebenzi be-SUNTOP, senze ngezifiso ukuzondla nokuzitholela ngokuphelele umshini wokusika we-CNC fiber laser uphumelele ukufakwa eFrance.
Ijubane eligijimayo lokulayisha nokulayishwa kuyashesha kakhulu, okuyizikhathi ezi-2 zokulayisha nokuthulula uhlobo lwe-cantilever eJalimane e-workshop efanayo. Ikhasimende lineliseke kakhulu ngobuchwepheshe be-SUNTOP yethu.
Muva nje i-SUNTOP ithuthukise ngempumelelo uhlelo lokuphakela nokuthulula oluzenzakalelayo ngokuphelele olunamandla angu-2500KG afanele ukulayishwa nokulayishwa kwensimbi okukhulu futhi okukhulu, izokonga kakhulu izindleko zabasebenzi, yenze indawo yokusebenzela inganakwa ngempela, futhi ibeke isisekelo esihle semboni 4.0.
Ngokombono wabadayisi bezimakethe, ukungeniswa nokuthunyelwa kwamabhizinisi azimele kukhuphuke kakhulu, futhi indima yezohwebo lwangaphandle “yokusimamisa” yayigqame kakhulu. Imininingwane ikhombisa ukuthi ezinyangeni zokuqala eziyi-10, ukungeniswa nokuthunyelwa kwamabhizinisi azimele kufinyelele ku-12 trillion yuan, ukwanda ngo-10.5%, okubalwa ngama-46.2% wenani lonke lokuhweba langaphandle laseChina, ukwanda kwamaphesenti angu-3.9 amaphuzu ngesikhathi esifanayo ngonyaka odlule . Phakathi kwabo, ukuthekelisa kwakungu-7.94 trillion yuan, ukwanda ngo-10.9%, kubalwa u-55.4% wenani eliphelele lokuthumela ngaphandle; ukungeniswa bekuyi-yuan engu-4.06 trillion yuan, inyuke ngo-9.7%, ebala u-35% wenani eliphelele lokungenisa.
Uma sibheke phambili esikhathini esizayo, kulindeleke ukuthi ukuhwebelana namanye amazwe onyakeni wonke kuzoqhubeka nokugcina isimo sizinzile futhi sihle. UTang Jianwei, umcwaningi oyinhloko wesikhungo sokucwaninga ngezezimali seBhange lezokuxhumana, uthe inani lokungenisa kanye nentengo yensimbi yensimbi, ubhontshisi wesoya kanye nezinye izinto ezinkulu zenyukile, okukhombisa ukuthi isidingo sasekhaya asikabi buthakathaka. Inkomba yokungenisa i-PMI ngo-Okthoba yayingu-50.8%, amaphesenti angu-0.4 amaphuzu aphezulu kunalawo enyanga eyedlule, futhi yayingaphezulu komugqa wokuqhuma nezinyanga ezimbili ezilandelanayo. Ngokutholwa kokusetshenziswa kwasekhaya kanye nesidingo sokukhiqiza, ukungenisa okulandelayo kulindeleke ukuthi kuqhubeke.
Ngokombono wabadayisi bezimakethe, ukungeniswa nokuthunyelwa kwamabhizinisi azimele kukhuphuke kakhulu, futhi indima yezohwebo lwangaphandle “yokusimamisa” yayigqame kakhulu. Imininingwane ikhombisa ukuthi ezinyangeni zokuqala eziyi-10, ukungeniswa nokuthunyelwa kwamabhizinisi azimele kufinyelele ku-12 trillion yuan, ukwanda ngo-10.5%, okubalwa ngama-46.2% wenani lonke lokuhweba langaphandle laseChina, ukwanda kwamaphesenti angu-3.9 amaphuzu ngesikhathi esifanayo ngonyaka odlule . Phakathi kwabo, ukuthekelisa kwakungu-7.94 trillion yuan, ukwanda ngo-10.9%, kubalwa u-55.4% wenani eliphelele lokuthumela ngaphandle; ukungeniswa bekuyi-yuan engu-4.06 trillion yuan, inyuke ngo-9.7%, ebala u-35% wenani eliphelele lokungenisa.
Uma sibheke phambili esikhathini esizayo, kulindeleke ukuthi ukuhwebelana namanye amazwe onyakeni wonke kuzoqhubeka nokugcina isimo sizinzile futhi sihle. UTang Jianwei, umcwaningi oyinhloko wesikhungo sokucwaninga ngezezimali seBhange lezokuxhumana, uthe inani lokungenisa kanye nentengo yensimbi yensimbi, ubhontshisi wesoya kanye nezinye izinto ezinkulu zenyukile, okukhombisa ukuthi isidingo sasekhaya asikabi buthakathaka. Inkomba yokungenisa i-PMI ngo-Okthoba yayingu-50.8%, amaphesenti angu-0.4 amaphuzu aphezulu kunalawo enyanga eyedlule, futhi yayingaphezulu komugqa wokuqhuma nezinyanga ezimbili ezilandelanayo. Ngokutholwa kokusetshenziswa kwasekhaya kanye nesidingo sokukhiqiza, ukungenisa okulandelayo kulindeleke ukuthi kuqhubeke.
Isikhathi Iposi: Jul-28-2020


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Sizokunikeza izeluleko ezisezingeni eliphezulu kakhulu kanye nekhotheshini yomkhiqizo.
Yiwu wholesale marketiyimakethe ethengisa izinto ezincane ezikhethekile etholakala e-Yiwu, e-Zhejiang.Ngo-2005, yabizwa ngokuthi "imakethe yempahla encane enkulu kunazo zonke emhlabeni".Ungabona zonke izinhlobo zezimpahla, njengezidingo zansuku zonke, izingubo nezicathulo, ikhishi le-hardware kanye nendlu yokugezela, izinto ezisetshenziswayo zasendlini ezincane, izipho zezandla nokunye.
Manje inendawo yebhizinisi engaphezu kwamamitha-skwele angu-800,000, amadokodo angaphezu kuka-34,000, kanye nokugeleza kwabagibeli kwansuku zonke okungaphezu kuka-200,000.Kuyisizinda esikhulu kunazo zonke saseShayina sokuthekelisa sezimpahla ezincane.
I-Yiwu International Trade City District 1
Isifunda sokuqala se-Yiwu Trade City sabeka isisekelo ngo-Okthoba 2001 futhi saqala ukusebenza ngokusemthethweni ngo-Okthoba 22, 2002. Imakethe ihlanganisa indawo engamahektha angu-420, indawo yokwakha engu-340,000 square metres, kanye nokutshalwa kwezimali okuphelele kwezigidi ezingu-700 zamayuan.Ihlukaniswe ngemakethe enkulu kanye nesikhungo sokuthengisa esiqondile samabhizinisi okukhiqiza., Isikhungo sokuthengwa kwempahla, isikhungo sokugcina, isikhungo sokupheka izindawo ezinhlanu zebhizinisi, ingqikithi yamadokodo angaphezu kuka-10,000, amakhaya amabhizinisi angaphezu kuka-10,500.
Isitezi esingu-1: izimbali zokwenziwa, izesekeli zezimbali, amathoyizi aluhlaza, amathoyizi aphephethekayo, amathoyizi kagesi, amathoyizi ajwayelekile, amathoyizi aholwa
Isitezi esi-2: isigqoko, ubucwebe
Isitezi esi-3: ubuciko bemikhosi, ubuciko bokuhlobisa, amakristalu e-porcelain, ubuciko bezokuvakasha, ozimele bezithombe
Isitezi esi-4: isikhungo sokuthengisa esiqondile semisebenzi yezandla, imihlobiso, izimbali, amabhizinisi okukhiqiza
I-YIWU INTERNATIONAL TRADE CITY DISTRICT 2
District 2 of Yiwu International Trade City China Yiwu International Trade City District 2 yavulwa ngo-Okthoba 22, 2004. Imakethe ihlanganisa indawo engamahektha angama-483, indawo yokwakhiwa engaphezu kuka-600,000 square metres, futhi inezitolo ezingaphezu kuka-8,000 nangaphezulu. Imindeni yamabhizinisi ayi-10,000.... Imakethe ifakwe izakhiwo zezentengiselwano, izakhiwo zamahhovisi, amahhotela ezinkanyezi ezine, nezikwele ezimbili empumalanga nasentshonalanga, futhi kuvulwe ibhasi lokubuka indawo lomugqa wendandatho.
Isitezi esingu-1: imithwalo, i-poncho, i-raincoat, isikhwama sokupakisha
2floor: amathuluzi ehadiwe, izesekeli, izingidi, imikhiqizo kagesi, imikhiqizo yezimoto
Isitezi esi-3: ikhishi lehadiwe negumbi lokugezela, izinto zikagesi ezincane zasendlini, okokusebenza kwezokuxhumana ngocingo, amawashi, amathuluzi kagesi
I-4floor: ihadiwe, imikhiqizo yangaphandle kanye nogesi, ukuthengiswa okuqondile kwasefekthri
5 Floor: Inhlangano Yezohwebo Zangaphandle
Uyafuna ukuthenga imikhiqizo emakethe ye-Yiwu?
I-YIWU INTERNATIONAL TRADE CITY DISTRICT 3
Isifunda sesi-3 se-Yiwu International Trade City, eShayina sinendawo yokwakha engu-460,000 square metres.Isitezi sokuqala kuya kwesesithathu sinamadokodo ajwayelekile angaphezu kuka-6,000 angama-square metres ayi-14, kanti indawo yesine kuya kweyesihlanu inamadokodo okuhweba angaphezu kuka-600 angama-80-100 square metres.Isitezi sesine sithengiswa ngqo ngabakhiqizi.Phakathi nendawo, izimboni ezingenayo yizimpahla zamasiko, zemidlalo, izimonyo, izibuko, oziphu, izinkinobho, izesekeli zokugqoka nezinye izimboni.Kuneziphephetha-moya ezimaphakathi, amasistimu enethiwekhi ye-broadband, i-TV ye-inthanethi, izikhungo zedatha, nezikhungo zokuqapha ukuphepha komlilo emakethe.
5F:Imidwebo/Uhlaka
I-4F:Izitolo Zefekthri-Izimonyo/Ubuhle/ImikhiqizoIzitolo zaseFactory-izimpahla zemidlalo nezinto zokubhala/imikhiqizo yangaphandleIzitolo Zokudayisa-impahla
3F:I-Mirror & CommbButton & ZipperIzesekeli ZezimonyoImikhiqizo YobuhleIzimpahla ZokugqokaIzesekeli
2F:Imikhiqizo Yezokungcebeleka Nezokuzijabulisa Ihhovisi Lempahla Yezemidlalo Nezincwadi Zokufunda
1F: Ipeni & Uyinki & Izibuko Zamehlo Zephepha
-1F:Isithombe Sonyaka Omusha,Ikhalenda Yasodongeni&Couplet
I-YIWU INTERNATIONAL TRADE CITY DISTRICT 4
I-Fourth District Market ye-International Trade City iyimakethe yesizukulwane sesithupha ye-Yiwu China Commodity City, enendawo yokwakha engu-1.08 million square metres, izitolo ezingaphezu kuka-16,000, kanye nezinkampani zamabhizinisi ezingaphezu kuka-20,000.Isitezi sokuqala semakethe sithengisa i-hosiery;esitezi sesibili kudayiswa izidingo zansuku zonke, amagilavu, izigqoko, nokunye ukotini yenaliti;Isitezi sesithathu sithengisa izicathulo, intambo, intambo, i-tie, uvolo, amathawula;Isitezi sesine sidayisa obhodisi, amabhande, nezikhafu;Esitezi sesihlanu, kwakhiwa isikhungo sokuthengisa esiqondile samabhizinisi okukhiqiza kanye nesikhungo sokuthenga izivakashi.
I-5F: Izidingo Zansuku zonkeIzimbathoEzokuvakasha Nesikhungo SokuthengaUhlaka/Izinsiza
4F:BeltBra & UnderwearScarf
3F:CaddiceTowelThread & TapeShoesLaceTie
2F: I-Knitted GoodsHat & CapGlovesDaily NecessitiesEarmuffs
1F: Amasokisi/Ama-Leggings
I-YIWU INTERNATIONAL TRADE CITY DISTRICT 5
5F:Izinkonzo Ze-inthanethiIzitolo ezingokoqobo
I-4F:Izesekeli Zemoto NesithuthuthuIzidingo ZemotoUkusabalalisa Kwempahla
I-3F:Indwangu YekhethiniIndwangu Eluthiwe Eyakhiwe
2F:I-BeddingChinese KnotDIY Handicraft
1F:Umbukiso Wemikhiqizo Yase-Afrika Nesikhungo SohweboICM-Imihlobiso/Imisebenzi yezandlaICM-Izingubo/Okusebenziseka nsuku zonkeICM-Ukudla/Imikhiqizo EnempiloEzinye Izimpahla Ezingenisiwe


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Le migomo nemibandela yokuthengisa ingenelwe yi-GHO AHK SPRL (0699.562.515) isihlalo sitholakala eBOULEVARD EDMOND MACHTENS 172 Box 1 1080 MOLENBEEK-SAINT-JEAN BELGIUM ngemuva kwalokhu ebizwa ngeGHO AHK SPRL kanti ngakolunye uhlangothi noma umuntu osemthethweni ofisa ukuthenga nge-GHO AHK SPRL iwebhusayithi ezobizwa ngokuthi "umthengi".
Into:
The imibandela yamanje yokuthengisa kuhlose ukuchaza ubudlelwano besivumelwano phakathi kwe-GHO AHK SPRL nomthengi kanye nemibandela esebenzayo kunoma yikuphi ukuthenga okwenziwe nge-GHO AHK SPRL, noma ngabe umthengi uchwepheshe noma umthengi. Ukutholwa kwempahla enhle noma insizakalo ngalesi siza samanje kusho ukwamukelwa ngaphandle kwesibambiso ngumthengi wale mibandela yokuthengisa. Lezi imibandela yokuthengisa izonqoba kunoma yiziphi ezinye izimo ezijwayelekile noma ezikhethekile ezingavunyelwe ngokucacile yi-GHO AHK SPRL. IGHO AHK SPRL iyaligodla ilungelo lokushintsha izimo zayo zokuthengisa nganoma yisiphi isikhathi. Kulesi simo, izimo ezisebenzayo kuzoba yilezo ezisebenza ngosuku loku-oda ngumthengi. Izici zezimpahla nezinsizakalo ezinikezwayo: Imikhiqizo kanye nezinsizakalo ezinikezwayo yilezo ezibalwe kukhathalogi eshicilelwe ku-GHO AHK SPRL. Le mikhiqizo nezinsizakalo zinikezwa ngaphakathi kwemikhawulo yamasheya atholakalayo. Umkhiqizo ngamunye uhambisana nencazelo eyenziwe ngumhlinzeki. Izithombe ezikwikhathalogi zithembeke ngangokunokwenzeka kepha azikwazi ukuqinisekisa ukufana okuphelele nomkhiqizo onikelwayo, ikakhulukazi maqondana nemibala.
amanani:
Amanani kukhathalogi amanani afaka i-VAT, kucatshangelwa i-VAT esebenzayo ngosuku lwe-oda; KWI-BELGIUM, KWAMANYE AMAZWE AManani entengo akhokhisiwe, noma yiluphi ushintsho esilinganisweni lungakhonjiswa entengo yemikhiqizo noma izinsizakalo.
I-GHO AHK SPRL iyaligodla ilungelo lokushintsha amanani ayo nganoma yisiphi isikhathi, inqobo nje uma intengo efakwe kuhlu kukhathalogi ngosuku lwe-oda kuzoba yiyo kuphela esebenzayo kumthengi.
Izintengo ezicashunwe zifaka phakathi "noma azibandakanyi" izindleko zokucubungula ama-oda, ezokuthutha kanye nokulethwa uma nje zenzeka ezindaweni ezinikezwe ngezansi.
Ama-oda:
Umthengi ofuna ukuthenga umkhiqizo noma insizakalo kufanele:
- gcwalisa ifomu lokuhlonza azokhombisa kulo yonke imininingwane eceliwe noma anikeze inombolo yekhasimende lakhe uma enayo;
- gcwalisa ifomu loku-oda online unikeze zonke izinkomba zemikhiqizo noma amasevisi akhethiwe;
- qinisekisa i-oda lakho ngemuva kokulihlola;
- ukhokhe ngaphansi kwezimo ezinqunyiwe;
- qinisekisa i-oda lakho nenkokhelo yakho.
Ukuqinisekiswa kwe-oda kusho ukwamukelwa kwale mibandela yokuthengisa, ukuvuma ukuba nolwazi oluphelele nokuyekelwa kwezimo zayo zokuthenga noma ezinye izimo.
Yonke imininingwane enikeziwe kanye nokuqinisekiswa okurekhodiwe kuzofanele ubufakazi bokuthengiselana. Isiqinisekiso sizokufanelekela ukusayina nokwamukela ukuthengiselana. Umthengisi uzoxhumana nge-imeyili isiqinisekiso se-oda elibhalisiwe.
Ukuhoxa:
Abathengi, abantu okungebona abangochwepheshe, bayazuza esikhathini sokuhoxa sezinsuku eziyi-14 kusukela ekulethweni kwe-oda labo lokubuyisela umkhiqizo kumthengisi ukuze atshintshisane noma abuyiselwe imali ngaphandle kwenhlawulo, ngaphandle kwezindleko zokubuyisa. Uma ukulethwa kungenziwa kungakapheli izinsuku ezingama-30, umthengi unelungelo lokukhansela ukuthenga futhi yonke inkokhelo kufanele ibuyiselwe ekhadini elifanayo elisetshenziselwe ukukhokha).
Inkokhelo imigomo:
Intengo ifanele lapho u-oda. Izinkokhelo zizokwenziwa ngekhadi lesikweletu; zizotholakala ngohlelo oluphephile lwe-PAY PAL olusebenzisa umthetho olandelwayo we-SSL "Secure Socket Layer" ukuze imininingwane edlulisiwe ibethelwe ngesoftware nokuthi akekho umuntu wesithathu ongayinaka ngesikhathi sokuhamba kwinethiwekhi. I-akhawunti yomthengi izodonswa kuphela uma kuthunyelwa imikhiqizo noma amasevisi atholakalayo kanye nenani lemikhiqizo noma amasevisi athunyelwe noma alandiwe. Ngokwesicelo somthengi, uzothunyelwa i-invoyisi yephepha ekhombisa i-VAT.
Ukudiliva:
Kudilivwa ekhelini eliboniswe kwifomu loku-oda elingaba sendaweni okuvunyelwene ngayo kuphela. Izingozi yisibopho somthengi kusukela lapho imikhiqizo ishiya indawo ye-GHO AHK SPRL. Uma kwenzeka umonakalo ngesikhathi sokuhamba, umbhikisho ocatshangelwe kahle kufanele wenziwe kumphathi zingakapheli izinsuku ezintathu zilethwe. Izikhathi zokulethwa zibonisa kuphela; uma zeqa ezinsukwini ezingamashumi amathathu kusuka ku-oda, inkontileka yokuthengisa ingaqedwa futhi umthengi abuyiselwe imali.
Isiqiniseko:
Yonke imikhiqizo enikezwe ngumthengisi iyazuza esiqinisekisweni esisemthethweni esinikezwe ngama-athikili 1641 nokulandela i-Civil Code.
Isibopho:
Uma kwenzeka ukungahambisani komkhiqizo okuthengisiwe, kungabuyiselwa kumthengisi ozoyibuyisa, ayishintshe noma ayibuyisele imali.
Zonke izimangalo, izicelo zokushintshaniswa noma zokubuyiselwa imali kufanele zenziwe ngeposi kuleli kheli elilandelayo: GHO AHK SPRL BOULEVARD EDMOND MACHTENS 172 Box 1 1080 MOLENBEEK-SAINT-JEAN BELGIUM zingakapheli izinsuku ezingamashumi amathathu zilethwe.
Okwenziwe ngenqondo:
Zonke izinto zewebhusayithi ye-GHO i-AHK SPRL futhi zihlala ziyizinto zobuhlakani nezikhethekile ze-GHO AHK SPRL.
Akekho ogunyaziwe ukukhiqiza kabusha, ukuxhaphaza, ukusakaza kabusha, noma ukusebenzisela noma iyiphi inhloso, noma yini, ingxenye yesayithi eyi-software, ebonakalayo noma ezwakalayo.
Noma yisiphi isixhumanisi esilula noma i-hypertext kuvinjelwe ngokuqinile ngaphandle kwemvume ebhaliwe ye-GHO AHK SPRL.
Imininingwane yomuntu:
Ngokuhambisana nomthetho ophathelene namakhompyutha, amafayela kanye nenkululeko kaJanuwari 6, 1978, imininingwane yohlobo lomuntu siqu ephathelene nabathengi ingahle ibe ngaphansi kokucutshungulwa okuzenzakalelayo. IGHO AHK SPRL iyaligodla ilungelo lokuqoqa imininingwane ngabathengi kufaka nokusebenzisa amakhukhi, futhi, uma ithanda, ukudlulisela kozakwethu bebhizinisi imininingwane eqoqiwe. Abathengi bangaphikisana nokudalulwa kwemininingwane yabo ngokwazisa IGHO AHK SPRL. Ngokufanayo, abasebenzisi banelungelo lokufinyelela nokulungisa idatha ephathelene nabo, ngokuya ngomthetho kaJanuwari 6, 1978.
Ukufaka kungobo yomlando - Ubufakazi:
I-GHO AHK SPRL izogcina ama-oda wokuthenga kanye nama-invoice ngokugcina ukwesekwa okuthembekile nokuqinile okwakha ikhophi elithembekile ngokuya ngemigomo ye-athikili 1348 ye-Civil Code.
Amarejista asekhompyutheni we-GHO AHK SPRL azobhekwa amaqembu njengobufakazi bokuxhumana, ama-oda, izinkokhelo nokuthengiselana phakathi kwamaqembu.
Isimangalo:
Izimo zamanje zokuthengisa kulayini zingaphansi komthetho waseBelgium.
Uma kunempikiswano, amandla anikezwa izinkantolo ezifanele zaseBrussels 1000 BELGIUM, ngaphandle kobuningi babamangalelwa noma isimangalo sewaranti.
Isignesha:
Thierry REMY:
Ummeli wezomthetho