History o pākoki: putanga me te whanaketanga

He mea paihere hītori Trigonometry ki tātai arorangi, no te mea he reira ki te whakatau i te mau tamataraa o tenei pūtaiao onamata, timata pūtaiao ki te tūhura i te hononga o ngā taurangi rerekē i roto i te tapatoru.

Ki te rā, pākoki ko te Micro-pāngarau, ako te hononga i waenganui i te uara o te koki me te roa o nga taha o te tapatoru, me te pā ana ki te tātari o ngā tuakiri taurangi o ngā pānga pākoki.

Ko te wā "pākoki"

Ko te wā, i hoatu ingoa ki tenei wāhanga o te pāngarau, i kitea tuatahi i roto i te taitara o te pukapuka fa'u e te Tiamana mathematician Pitiskusa i 1505. Ko te kupu "pākoki" Ko o take Kariki me te tikanga o "ki te ine i te tapatoru." Hei hei atu pau, ehara i te mea he taha mau o tenei ahua, engari e pā ana ki tona whakatau, e ko, te whakatau i te uara o ona āhuatanga unknown whakamahi mohiotia.

mōhiohio General e pā ana ki pākoki

timata hītori pākoki neke atu i a piti miliniuma i. I te tīmatanga, e pā ana tona takanga i ki te hiahia ki te whakatau i nga koki o te tapatoru, me te ōwehenga āhuatanga. I roto i te rangahau ka reira mārama e titau te faaiteraa pāngarau o enei whanaunga te whakataki o ngā pānga pākoki motuhake, i te tuatahi i hanga e i roto i rite te tepu tau.

He tokomaha hoki i whakauru sciences ki hiringa pāngarau ki te whanaketanga o te pākoki i ïa hītori. wae Origin koki inenga (nekehanga) e pā ana ki te pūtaiao rangahau o Papurona tahito, e hāngai ana i runga i te pūnaha sexagesimal o tātai, i hoatu ara ki te hou te ira, whakamahia i roto i te maha tikanga ka whakamahia.

Kei te riro te reira e vai tuatahi hei wāhanga o te pākoki tātai arorangi. Katahi ia ka anga ki te whakamahi i roto i te hoahoanga. A i runga i te wā, i reira ko te whai take o tenei pūtaiao i roto i mara ngā o te mahi a te tangata. Tenei, i roto i ngā, arorangi, moana me te rangi navigation, Acoustics, optics, hikohiko, hoahoanga me etahi atu.

Pākoki i roto i te mau tenetere wawe

Te arata'ihia e te raraunga pūtaiao i runga i te pukahu ora, mutu nga kairangahau e pā ana te hītori o te putanga o te pākoki te ki te mahi o te arorangi Kariki Hipparchus, e whakaaro tuatahi i runga i te kimi huarahi ki te whakaoti tapatoru (porohita). no ana mahi ki te BC rau 2.

Ko hoki reira tetahi o nga whakatutukitanga tino nui o taua wa, ko te ki te whakatau i te ōwehenga o te waewae, me te tāroa i roto i te tapatoru tika nei i muri ka mohiotia rite te Pythagoras Theorem.

e pā ana te hītori o te whanaketanga o te pākoki i Kariki tawhito te ki te ingoa o te arorangi Ptolemy - te kaituhi o te pūnaha geocentric o te ao i taea ana te aroaro o Nīkara.

kihai i arorangi Kariki mohiotia aho, whenu , me te pātapa. whakamahia ratou tepu ki te kitea te uara o te rauoro o te porowhita mā te whakamahi i te pewa contractible. Ko te wae o te ine i nekehanga tangiata, meneti me hēkona. i rite ki te pūtoro wahi sixtieth kotahi tohu.

Ano, ka whakanekehia ake rangahau o nga Kariki onamata te whanaketanga o te pākoki porohita. I roto i ngā, Euclid i tona "Elements" tauwehe arata'i i runga i regularities ōwehenga rōrahi o pōro o ngā diameters. Kua riro ana mahi i roto i tenei mara i te ahua o te hihiko ki te whanaketanga o ake me pātata wāhanga o te matauranga. Tenei, i roto i ngā, i te hangarau o mea arorangi, te ariā o haurangi mahere, taunga tiretiera pūnaha, me pera i runga i. D.

Anotau Middle: te ako o pūtaiao Indian

Tino ahu whakamua tutuki arorangi Indian wharekarakia. Ko te mate o te pūtaiao tawhito i roto i te rau tau IV arahina ki te nekehanga i roto i te whanaketanga o te pāngarau i roto i India.

timata te hītori o te putanga o te pākoki rite te wāhanga motuhake o te mahi pāngarau i roto i nga Anotau. Ko te ka whakakapi te kaimātai pūtaiao te sinuses chord. Tenei kitea whakaaetia ki te tomo i te mahi e pā ana ki ngā akoranga taha me koki o te tapatoru matau. E ko, ko reira na te timatanga wehe he pākoki i tātai arorangi, hoko he peka o te pāngarau.

Ko te tepu tuatahi o ngā sine i roto i Aryabhata, i puritia ratou i roto i te 3 ^o 4 ^o 5 ^{i runga.} I muri mai, i reira nga putanga taipitopito o te papa: i roto i ngā, arahina Bhaskara roto i kahore he tepu 1 ^runga.

puta te pukapuka motuhake tuatahi i runga i pākoki i roto i te rau tau X-XI. Ko tōna kaituhi ko te Central akonga Āhia al-Biruni. He kaituhi wharekarakia ake â i roto i tona mahi matua "Te Kēnana Mas'ud" (Buka III), i roto i te pākoki, he tepu o ngā sine (i roto i ngā āpiti o 15 ') me te tepu o te pātapa (i roto i ngā āpiti o te 1 °).

Ko te hītori o te whanaketanga o te pākoki i Europe

I muri i te whakawhitinga o Ngā tuhinga whakapae Arab ki Latin (XII-XIII c) te nuinga o nga whakaaro o pūtaiao Indian me Pahia tono i pūtaiao Pākehā. Ko te whakahua tuatahi o te pākoki no ki te rau tau XII i Europe.

E ai ki kairangahau, te hītori o te pākoki i Europe e pā ana ki te ingoa o Ingarihi Richard o Wallingford, nei ko te kaituhi o te mahi "wha o te pukapuka i runga i te rauoro hāngai, me te kōaro." E ko tona mahi te mahi tuatahi e te katoa i oti rawa ki pākoki. Na roto i te rau tau XV, he maha kaituhi i roto i to ratou tuhituhi whakahua nga ngā pānga pākoki.

History o pākoki: wā New

I roto i te wā hou, ka mōhio o te faufaa tino o te pākoki i roto i te tātai arorangi me te kōkōrangi kore anake, engari ano hoki i roto i te tahi atu wāhanga o te ora te nuinga o pūtaiao. Ko reira, te tuatahi, me te tuatahi, pū, tuku kōrero me te whakatere i runga i ngā haerenga moana roa. Na reira, i roto i te hawhe tuarua o te rau tau XVI, kua paanga tenei kaupapa maha iwi rongonui o taua wa, tae atu Nikolaya Kopernika, Ioganna Keplera, Fransua Vieta. ka mau Nīkara pākoki e rave rahi pene o tona pukapuka "I nga takaí o te Metua i ao" (1543). I muri mai, i roto i nga 60raa o te rau tau XVI, Retik - he akonga o Nīkara - hua i roto i tona "wāhanga Optical o Astronomy" pyatnadtsatiznachnye tepu pākoki.

Fransua Viet i roto i "Mathematical kēnana" (1579) homai he taipitopito me te pūnahanaha, ahakoa e keri, āhuatanga o te pākoki papatahi, me te porohita. Na ko Albrecht Dürer te sinusoid kotahi i roto i nei i whanau.

Ko te maitai Leonarda Eylera

Me te pākoki ihirangi hou me te momo o te nama ko Leonarda Eylera. kei tona pukapuka "Introduction ki te tātaritanga o te mure ore" (1748) he whakamāramatanga o te wā "pānga pākoki", i te mea ōrite ki te hou. Ko te kupu, i taea ki te whakatau i ngā mahi kōaro te kaipūtaiao. Otiia e kore e katoa te e.

Kua Whakamāramatanga o ngā pānga pākoki i runga i te raina tūturu kua meinga whakawhetai taea ki te rangahau Hēura kore anake koki kino whakaaetia, engari nga koki Bole 360 °. Ko te wā tuatahi kua whakamatauria e ia i roto i ana i tuhituhi ai e te hunga tōraro te whenu me te pātapa o te koki matau. Ko hoki Roha o whenu katoa, me te hara te kaiaka o tenei kaiputaiao. Ko te ariā whānui o te raupapa pākoki me te ako o te pūtahitanga o te raupapa whiwhi kahore he taonga o ngā tirohanga a te Hēura. Heoi, e mahi ana i runga i te otinga o ngā raruraru e pā ana, hanga ana e ia he tokomaha ngā āhuatanga i roto i tenei mara. i roto i tona mahi i haere tonu te reira e te hītori o pākoki. Poto i roto i ana i tuhituhi ai mahi ia ki ngā pātai, me te pākoki porohita.

tono pākoki

e kore te mea e pā ana ki te pūtaiao tono Trigonometry, i roto i te ora tūturu rā te reira whakamahia uaua mahi. Heoi, e kore e tenei meka whakaititia tona faufaa. He mea tino nui, hei tauira, he tikanga tapatorutia e taea arorangi ki rawa tika te ine i te tawhiti ki whetu whakaaro, me te aroturuki i ngā pūnaha amiorangi navigation.

Hoki, whakamahia pākoki te i roto i te whakaterenga, ariā waiata, Acoustics, optics, tātari o hokohoko pūtea, hikohiko, tūponotanga ariā, tatauranga, te koiora, rongoa (hei tauira, i roto i deciphering ultrasound ultrasound me tomography computed), pharmaceutics, matū, tau ariā, seismology, huarere , Oceanography, cartography, he maha ngā wāhi o te ahupūngao, mahere whenua me te geodesy, hoahoanga, mātauranga whakahua, ohaoha, engineering hiko, engineering aunoa, whakairoiro rorohiko, mātauranga tioata, a na i runga i. d. ko te hītori o te pākoki me tona tūranga i roto i te ako E ako enii tikanga tūturu, me te pāngarau ki tenei ra. Pea i roto i te heke mai, ka kia ara nui ona tono.

Ko te takenga mai o te ariā taketake

He neke atu i te rau tau i te hītori o te putanga me te whanaketanga o te pākoki. Ko te kupu whakataki o te ariā e hanga i te pūtake o tēnei wāhanga o te pāngarau, ano kahore i rangitahi kau.

Ko te kupu, ko te ariā o "hara" e he hītori rawa roa. E kitea whakahua o nga wāhanga ngā o te hononga o tapatoru me porowhita ara i roto i nga mahi pūtaiao, teiti i te BC III rau. Ko te mahi o taua aivanaa nui tahito rite Euclid, Archimedes, Apollonius o Pereka, kua roto i te ako tuatahi o enei whanaunga. ka ui āhuatanga hou te tetahi huringa terminological. Ko te kupu, homai te Indian pūtaiao Aryabhata te ingoa rauoro o "Jiva", oia hoi "aho". A, no te whakamaoritia Arab tuhinga pāngarau ki Latin, te wā tata whakakapi e te aho uara (m. E. "Bend").

puta te kupu "whenu" nui i muri. Tenei wā ko te whakarāpopototanga mo te kīanga Latin "aho atu".

pātapa tupu e pā ana ki wetemuna te raruraru o te whakatau i te roa o te atarangi. Ko te wā "pātapa" whakaurua i roto i te mathematician Arab X rautau Abu al-Wafa, wahi o nga papa o mua, ki te whakatau i te pātapa, me te pātapa taupoki. Otiia kihai i kaipūtaiao Pākehā mohio e pā ana ki enei whakatutukitanga. ringatohu mathematician Tiamana, me te arorangi Regimontan enei ariā i roto i te 1467 taunaki ana pātapa ture tauwehe - ki tona nama. He whakamāoritia te wā rite "mo".