History of trigonometry: chidzoke uye kukura

Trigonometry nhoroondo iri zvakabatana chaizvo pamwe nezvenyeredzi, nokuti kusangana nematambudziko ichi sainzi yekare, masayendisiti akatanga kuongorora ukama variables yakasiyana netriangle.

To musi, trigonometry chinhu Micro-masvomhu, kudzidza ukama pakati zvinokosheswa pamakona uye urefu panhivi zvokuridza, uyewo nezvokukunda kuongorora algebraic mazita ose trigonometric mabasa.

Shoko rokuti "trigonometry"

Shoko rokuti, akapa zita kuti chikamu ichi masvomhu, yakatanga kuwanikwa musoro bhuku rakanyorwa German yemasvomhu Pitiskusa muna 1505. Shoko "trigonometry" ane Greek mavambo uye rinoreva "kuyera netriangle." Kuti tive kunyatsoenderana, haisi divi chaiyo nhamba iyi, asi pamusoro wayo chisarudzo, kureva, kusarudza tsika yayo vasingazivikanwi zvinhu kushandisa kuzivikanwa.

General ruzivo pamusoro trigonometry

Trigonometry nhoroondo vakatanga zvemakore anodarika maviri apfuura. Pakutanga, chiitiko chacho aishamwaridzana kudikanwa kuona pamakona ose netriangle uye zvakaita reshiyo. Panguva tsvakurudzo zvakava pachena kuti akarongeka kuratidza ukama izvi zvinoda kutanga anokosha trigonometric mashandiro, izvo pakutanga vakaitwa senzira kusanganiswa tafura.

Nokuti vazhinji sungano sayenzi vane masvomhu zvakasimbisa kukura trigonometry chaiwo kare. Origin angled chipimo zviumbu (madhigirii) chokuita pakutsvakurudza nemasayendisiti Bhabhironi rekare, inobva sexagesimal gadziriro kukarukureta, iyo chamuita kuti ano ari grade, anoshandiswa sayenzi zhinji takanyorera.

Zvinofungirwa kuti pakutanga aivapo sechikamu trigonometry yezvenyeredzi. Zvadaro akatanga kushandiswa mapurani. Uye nokufamba kwenguva, paiva kushanda ichi nesayenzi muminda mabasa evanhu akasiyana. Izvi, zvikurukuru, nezvenyeredzi, gungwa uye mhepo navigation, acoustics, optics, zvemagetsi, mapurani uye nevamwe.

Trigonometry mu emakore okutanga

Kutungamirirwa mashoko kwesayenzi pamusoro vasara zvisaririra, vatsvakurudzi vakagumisa kuti nhoroondo kwaita trigonometry Rinobatanidzwa ne basa Greek zvomuchadenga Hipparchus, uyo kutanga acharangarira kutsvaka nzira yokugadzirisa zvokuridza (idenderedzwa). Mabasa ake ndezvaJehovha 2nd remakore BC.

Uyewo chimwe chezvinhu zvinokosha nebudiriro kuti nguva yava kuona nhamba makumbo uye hypotenuse mune netriangle zvakanaka izvo akazozivikanwa sezvo Pythagorean Theorem.

Nhoroondo kukura trigonometry muGirisi yekare chokuita nezita zvomuchadenga Ptolemy - munyori ari geocentric ino nyika kuti akunda pamberi Copernicus.

vanodzidza nezvenyeredzi Greek havana kuzivikanwa Sine, cosine uye tangent. Vaishandisa pamatafura kuwana kukosha Chord of denderedzwa vachishandisa contractible chinhu chakakombama. The zviumbu yakayerwa vaiva nevaya madhigirii, maminitsi nemasekonzi. Mumwe dhigirii akanga akaenzana sixtieth mugove nharaunda.

Uyewo, zvidzidzo vaGiriki vekare akasimudzira kukura idenderedzwa trigonometry. Zvikurukuru, Euclid mu "Elements" ake theorem no kunotungamirira pamusoro regularities ratios Vhoriyamu balls ose diameters siyana. mabasa ake mumunda ichi zvazova yorudzii zvairatidza kuti pave zvakawanda uye pedyo dzine ruzivo. Izvi, kunyanya, mabikirwo muchadenga zviridzwa, dzidziso mepu maberere, yokudenga batanidza maitiro, uye zvichingodaro. D.

Middle Ages: kudzidza masayendisiti Indian

Zvinokosha mberi kubudirira Ages Indian nyanzvi. Rufu yekare nesayenzi ari IV remakore zvakakonzera chaishanda kukura wemasvomhu kuIndia.

Nhoroondo kwaita trigonometry sezvo yoga Chikamu kwemasvomhu muviri mumwe akatanga kuMiddle Ages. Ndipo apo masayendisiti chakatsiva nevaya sinuses. Izvi zvakawanikwa kubvumirwa kupinda mabasa chokuita zvidzidzo kumativi uye pamakona ose netriangle zvakanaka. Kureva, zvakanga ipapo pakutanga kuzviparadzanisa trigonometry kubva nezvenyeredzi, kuva bazi wemasvomhu.

Tafura sines vokutanga vaiva Aryabhata, dzaiitwa ^{3 4} 5 ^pamusoro. Gare gare, paiva hwakadzama shanduro matafura: zvikurukuru, Bhaskara akatungamirira kuburikidza Sine tafura 1 ^pamusoro.

Yokutanga kushandiswa yekutanga iri trigonometry chakaonekwa X-XI remakore. munyori wayo aiva Central Asian nyanzvi al-Biruni. A Ages munyori zvakawanda kunokura mubasa rake guru "The Canon Mas'ud" (Book III), mu trigonometry, tafura sines (mu increments 15 ') uye tafura tangents (mu increments 1 °).

Nhoroondo kukura trigonometry mu Europe

Pashure kuchinjwa Arab akadhindwa yechiLatin (XII-XIII c) vakawanda pfungwa masayendisiti Indian uye Persian vakanga rakumbirwa European nesayenzi. The kutaurwa trigonometry rokutanga ndezvaJehovha XII remakore muEurope.

Maererano nevaongorori, nhoroondo trigonometry mu Europe chokuita nezita wokuEngland Richard pakati Wallingford, uyo aiva munyori mabasa "Four ari bhuku iri zvakananga uye inverted chords or the." Kuti basa rake rakanga riri basa rokutanga kuti rwunokwanisa vakazvipira trigonometry. By XV remakore, vanyori vakawanda zvavainyora nezvemwoyo trigonometric mabasa.

History of trigonometry: New nguva

Munguva dzazvino, masayendisiti akawanda vakaziva yokuoma kukosha trigonometry kwete chete nezvenyeredzi uye nyeredzi, asiwo mune mamwe mamiriro ezvinhu oupenyu. Zviri, pakutanga, atirari, optics uye kufamba pamusoro refu mugungwa Reisen. Saka, yechipiri yezana XVI remakore, nyaya iyi yave kuziva vakakurumbira vanhu vazhinji iyoyo, kusanganisira Nikolaya Kopernika, Ioganna Keplera, Fransua Vieta. Copernicus akatora trigonometry wandei muzvitsauko bhuku rake "Pazuva nokumukirana pakati Spheres Vekudenga" (1543). Gare gare, muna 60s ari XVI remakore, Retik - mudzidzi Copernicus - zvichizoita ake "Optical Chikamu Astronomy" pyatnadtsatiznachnye trigonometric pamatafura.

Fransua Viet mu "kwemasvomhu seakafuridzirwa" (1579) anotaura mashoko akakwana uye hurongwa, kunyange unproven, hunhu flat uye idenderedzwa trigonometry. Uye Albrecht Dürer ndiye kuburikidza kwakazvarwa sinusoid.

The dhigirii Leonarda Eylera

Kupa trigonometry ano kugutsikana uye mhando mbiri raiva Leonarda Eylera. bhuku rake "Nhanganyaya kuongorora kusingaperi" (1748) rine tsanangudzo rokuti "trigonometric mashandiro", iro rinoreva kuti ano. Saka, musayendisiti akakwanisa kuona Ivan Kuchin mabasa. Asi kwete ndizvozvo zvose.

Definition of trigonometric mashandiro ari mutsetse chaiye chakaiswa zvibvire ndatenda kutsvakurudza Euler kwete chete bvumidzwa kunaka pamakona, asi pamakona Bole 360 °. Yaiva nguva yokutanga akaratidza muzvinyorwa zvake kuti cosine uye tangent ane kodzero angled zviri kunaka. Kuwedzera yose cosine uye Sine akanga kukosha musayendisiti ichi. The vakawanda Dzidziso trigonometric dzinotevedzana uye kudzidza convergence pane akatevedzana vakawana havasi vanovengwa Euler kuti kuferefeta. Zvisinei, kushanda kugadzirisa zvinetso kufanana, akaita zvinhu zvakawanda mumunda uyu. Rakanga kuburikidza basa rake rakanga zvakaramba munhoroondo trigonometry. Muchidimbu zvaakanyora yaakabata nayo mibvunzo uye idenderedzwa trigonometry.

mafomu trigonometry

Trigonometry hakusi akarondedzera sayenzi vakashandisa, mune chaiyo muupenyu zviri Kashoma kushandiswa mabasa. Zvisinei, chokwadi ichi hazvirevi kutapudza kukosha kwayo. Zvakakosha chaizvo Somuenzaniso, imwe triangulation nzira inoita vanodzidza nezvenyeredzi zvakarurama kwazvo kuyera daro nenyeredzi nepfungwa uye akuteerere wekushandisa Satellite enyika.

Uyewo, trigonometry inoshandiswa navigation, mumhanzi dzidziso, acoustics, optics, kuongorora misika yemari, zvemagetsi, mukana dzidziso, nhamba, zvipenyu, mushonga (somuenzaniso, achiongorora zvaive Ultrasound Ultrasound uye computed tomography), pharmaceutics, kemisitiri, nhamba dzidziso, seismology, meteorology , oceanography, cartography, nzvimbo dzakawanda wefizikisi, kwakaita nzvimbo yacho uye geodesy, mapurani, phonetics, dzezvoupfumi, zvemagetsi engineering, zvokuimba engineering, kombiyuta Graphics, crystallography, uye zvichingodaro. d. nhoroondo trigonometry wayo muchinangwa kudzidza sayenzi enii dzinongoitika uye akarongeka vari vakadzidza nanhasi. Zvichida munguva yemberi, mafomu ayo achava yakatokura.

Kwakatangira dzinokosha pfungwa

Nhoroondo chidzoke uye kukura trigonometry ane anopfuura zana. Kutanga pfungwa zvinoumba hwaro muchikamu ichi masvomhu, uyewo akanga asina chinguva.

Saka, pfungwa "chivi" rine refu chaizvo nhoroondo. Muchirumbidza siyana zvikamu zviri ukama zvokuridza uye madenderedzwa zvinowanika kunyange mabasa zvesainzi, kudanana kubva III remakore BC. Mabasa nyanzvi huru yakadai yekare sezvo Euclid, Archimedes, Apollonius pamusoro kuPega, kare ane kudzidza ukama izvi kutanga. New zvakawanwa vakakumbira mumwe kuchinja terminological. Nokudaro, Indian musayendisiti Aryabhata anopa Chord zita "Jiva", zvichireva "bowstring". Kana Arab kwemasvomhu magwaro akashandurwa yechiLatin, shoko pedyo yatsiviwa ukoshi Sine (m. E. "Bend").

Shoko "cosine" akazviratidza zvikuru gare gare. Ichi ndechimwe chinhu chidimbu kuti Latin okuti "mamwe Sine".

Chiitiko tangents chokuita decoding dambudziko kuziva urefu kwomumvuri. Shoko rokuti "tangent" wakatangwa muna Arab yemasvomhu X remakore Abu al-inopindapaiyeseiyo, chikamu chokutanga pamatafura kuziva tangent uye cotangent. Asi masayendisiti European havana kuziva kubudirira izvi. yemasvomhu German uye zvomuchadenga Regimontan rediscovers izvi pfungwa muna 1467, uchapupu theorem no pakati tangents - yake chikwereti. A ashandura izwi se "bata".