History of kwitrigonometri: kokuhluma kunye nophuhliso

Imbali kwitrigonometri kuhlangene ne ngeenkwenkwezi, kuba ngayo ukuhlangabezana nemingeni kwale nzululwazi yamandulo, oososayensi baqalisa ukuhlola ukuzalana variables ezahlukeneyo unxantathu.

Ukuza kuthi ga ngoku, kwitrigonometri yi Micro-imathematika, ukufunda ulwalamano phakathi amaxabiso engile kunye ubude emacaleni oonxantathu, kwakunye zokujongana uhlahlelo zengqwalaselo aljibra kwemisebenzi netrigonometri.

Igama elithi "kwitrigonometri"

Igama elithi, awamnika igama kule candelo yemathematika, kwafunyanwa yokuqala kwisihloko sencwadi yabhalwa German yezibalo Pitiskusa ngo-1505. Igama elithi "kwitrigonometri" livela kwisiGrike yaye lithetha "ukuba umlinganiselo unxantathu." Ukuze ube ngqo ngakumbi, kuba akukho njengomlinganiso ngokoqobo lo mzobo, kodwa isigqibo sayo, oko kukuthi, nokumisela iinqobo lweziqalelo zayo ongaziwayo ngokusebenzisa ezaziwayo.

ulwazi ngokubanzi malunga kwitrigonometri

Imbali kwitrigonometri yaqala zeminyaka ngaphezu emibini eyadlulayo. Ekuqaleni, ukwenzeka kwayo ezinxulumene imfuneko ukuqinisekisa engile kanxantathu kunye aspect. Ngethuba lokwenza uphando kwacaca ukuba ibinzana yemathematika ezi ubudlelwane kufuna ukuqaliswa zemisebenzi eyodwa netrigonometri, leyo ekuqaleni wenziwa phandle itafile lwamanani.

Kuba Sciences ezininzi nozimanya ngokupheleleyo kunye okuqhubela imathematika kuphuhliso kwitrigonometri yile imbali. iiyunithi imvelaphi angle womlinganiselo (degrees) ezinxulumene ne izazinzulu zophando waseBhabhiloni yamandulo, isekelwe kwinkqubo sexagesimal yokubala, nto leyo eyabangela ukuba mihla kwesishumi, esetyenziswa zenzululwazi ezininzi enokusebenziseka.

Kuthathwa ukuba ekuqaleni wabakho njengenxalenye kwitrigonometri ngeenkwenkwezi. Emva koko waqala ukuba kusetyenziswa bokwakha. Kwaye phezu kwexesha, kwakukho ukubaluleka kwale nzululwazi kwiinkalo ezahlukeneyo zezinto ezenziwa luluntu. Oku, ingakumbi, ngeenkwenkwezi, ulwandle navigation umoya, umsindo, ngokukhanya, elektroniki, izakhiwo, kunye nezinye.

Kwitrigonometri emakhulwini okuqala

Bakhokelwa data lwenzululwazi izinto ezingcwele abasindileyo, abaphengululi bagqiba kwelokuba kwimbali ukuvela kwitrigonometri unxulunyaniswa umsebenzi ngeenkwenkwezi Greek Hipparchus, ngubani kuqala wacinga ekufumaneni iindlela zokusombulula oonxantathu (ukulenza). imisebenzi zakhe zivela BC ngenkulungwane yesi-2.

Kwakhona enye mpumelelo ibalulekileyo elo xesha kukuba ukumisela umlinganiselo imilenze kunye hypotenuse kwi unxantathu okulungileyo kamva yaziwa ngokuba kaPythagoras theorem.

Imbali zophuhliso kwitrigonometri e Greece yamandulo linxulunyaniswa igama ngeenkwenkwezi Ptolemy - umbhali kwenkqubo geocentric zehlabathi ezazikho phambi uCopernicus.

Izazi isiGrike ayaziwa sine, cosine netangent. Basebenzisa iitafile ukufumana ixabiso Isingqi wesangqa usebenzisa i arc contractible. Iiyunithi zemilinganiselo bekukho izidanga imisindo, imizuzu nemizuzwana. Omnye degree wayelingana kwisinye ukuya kumashumi amathandathu inxenye radius.

Kwakhona, izifundo yamaGrike amandulo ikhuthaze uphuhliso kwitrigonometri ukulenza. Ngokukodwa, Euclid ngo "Elements" theorem yakhe kukhokelela kwi regularities Umlinganiselo umthamo iibhola ze ngobubanzi ezahlukeneyo. imisebenzi yaKhe kule asendle abe ngonenceba ngokwentshukumisa kuphuhliso lwemimandla ngakumbi ezikufutshane ulwazi. Oku, ingakumbi, ubuchwepheshe kwezixhobo ngeenkwenkwezi, ingcamango uqikelelo imaphu Iziko ukulungelelanisa inkqubo, njalo-njalo. D.

Abanemvume: isifundo zezazinzulu Indian

inkqubela ebonakalayo azuzwe Indian izazi ephakathi. Ukufa nenzululwazi yamandulo kwinkulungwane IV kukhokelele kwishifti kuphuhliso kwemathematika India.

Imbali ukuvela kwitrigonometri njengoko icandelo elahlukileyo ukuzilolonga zemathematika yaqala kuMbindi Ages. Naso xa izazinzulu indawo sinuses usinga leyo. Le lokufumanisa bavunyelwe ukuba bangene imisebenzi enxulumene izifundo amacala nee-engile kanxantathu tye. Oko kukuthi, kwakunjalo ngoko ekuqaleni ukwahlula a kwitrigonometri kwinzululwazi ngeenkwenkwezi, waba isebe lemathematika.

Le yokuqala itheyibhile sines ezibe Aryabhata, bavalelwa ^{3 4 5.} Kamva, kwakukho iinguqulelo eneenkcukacha yezintlu: ingakumbi, Bhaskara ndamhambisa kulo sine itheyibhile ^1.

Eyokuqala imbali yokuqala kwanombolo kwitrigonometri uvele X-XI leminyaka. Umbhali saso Central umphengululi Asian al-Bīrūnī. A umbhali medieval ngakumbi ngakumbi umsebenzi wakhe omkhulu othi "The Canon Mas'ud" (Incwadi III), kwitrigonometri, itafile sines (ngokwemizuzu ka-15) kunye itheyibhile tangents (ngokwemizuzu 1 °).

Imbali zophuhliso kwitrigonometri eYurophu

Emva kokuba ukudluliselwa azibhala Arab zibe Latin (XII-XIII c) uninzi izimvo zezazinzulu Indian kunye Persian zaye ebolekiweyo nenzululwazi yaseYurophu. Sisihlandlo sokuqala kwitrigonometri fanele kwinkulungwane XII eYurophu.

Ngokutsho kwabaphandi, imbali kwitrigonometri eYurophu enxulumene ne igama eliNgesi Richard Wallingford, ngubani waba yimbangi imisebenzi "ezine ama kwi taxi ngqo kunye zocaphulo." Ukuba umsebenzi wakhe umsebenzi wokuqala into enikelwe ngokupheleleyo nezetrigonometry. Xa kwekhulu XV, ababhali abaninzi kwiincwadi zabo ukhankanye netrigonometri.

History of kwitrigonometri: ixesha New

Kule mihla, izazinzulu ezininzi yaba babenolwazi ngokubaluleka ebalulekileyo kwitrigonometri nje kuphela ngeenkwenkwezi ngeenkwenkwezi, kodwa nakwezinye iinkalo zobomi. Ngoko ke, kuqala, zokudubula, optic navigation kwi ukuhamba elide elwandle. Ngoko ke, kwisiqingatha sesibini senkulungwane XVI, lo mbandela benomdla Abantu abadumileyo abaninzi belo xesha, kuquka Nikolaya Kopernika, Ioganna Keplera, Fransua Vieta. Copernicus wathabatha kwitrigonometri izahluko ezininzi wakhe othi "Ngomhla Revolutions of the Sphere waseZulwini" (1543). Kamva, kwi 60s zenkulungwane XVI, Retik - ngumfundi Copernicus - okubangela 'Icandelo Optical of Astronomy' yakhe pyatnadtsatiznachnye iitafile netrigonometri.

Fransua Viet ngo "Mathematical Canon" (1579) unika eneenkcukacha ngendlela, nangona bokuba, uphawu le kwitrigonometri caba ukulenza. Kwaye Albrecht Dürer lo sinusoid omnye ngaye kwazalwa.

Nempikiswano Leonarda Eylera

Ukunika kwitrigonometri umxholo mihla kunye nohlobo yemali Leonarda Eylera. wakhe othi "Introduction to the uhlalutyo engenasiphelo" (1748) uqulathe inkcazo elithi "netrigonometri", oko kulingana ngexabiso mihla. Ngoko ke, lo nzulu yakwazi ukumisela imisebenzi nguqu. Kodwa loo nto bonke.

Inkcazzo netrigonometri kwi esqwini yonke lokwenene kwenzeka ngenxa uphando Euler iiengile Kuvumeleke ezimbi nje kuphela, kodwa engile Bole 360 °. Yayilixesha lokuqala uye wabonisa kwiincwadi zakhe ukuba cosine kunye tanjenti imo yekona lasekunene negative. Ukwandiswa cosine lonke kunye sine nayo ngokwemfanelo yalo nzulu. Imfundiso ngokubanzi series netrigonometri kunye nofundo yokuhlangabezana thotho ifunyenwe azikho izinto zophando Euler kaThixo. Noko ke, ukusebenza ngesisombululo iingxaki ezinxulumene, wenza izinto ezifunyaniswe ezininzi kule nkalo. Kwaba ngomsebenzi wakhe waqhubeka nomsebenzi kwimbali nezetrigonometry. Ngokufutshane ngemisebenzi yakhe awamphatha ngayo imibuzo kunye nezetrigonometry ukulenza.

izicelo kwitrigonometri

Kwitrigonometri hhayi ezihlobene yesayensi isetyenziswa, ebomini bemihla ngemihla ukuba kunqabile kusetyenziswa imisebenzi. Noko ke, le nto ayipheli ukubaluleka kwayo. Kubaluleke kakhulu, umzekelo, indlela triangulation evumela ngeenkwenkwezi ukulinganisa ngokuchanileyo umgama neenkwenkwezi nesidima kunye nokuhlola iinkqubo Hewana navigation.

Kwakhona, kwitrigonometri isetyenziswa inqanawa, theory umculo, umsindo, ngokukhanya, uhlalutyo kweemarike zemali, elektroniki, ithiyori ngokuqinisekileyo, amanani, ibhayoloji, iyeza (umzekelo, xa yonke ezama ultrasound ultrasound kunye Itomography ukubalwa), pharmaceutics, imichiza, ithiyori inombolo, ngezakhi, meteorology , eliJongene, cartography, iindawo ezininzi physics, isimo kunye geodesy, izakhiwo, ipateni yemizobo, ezoqoqosho, ubunjineli elektroniki, ngezobunjineli, imizobo computer, crystallography, njalo njalo. d. imbali kwitrigonometri kunye nendima yayo kuphononongo sciences enii zendalo zemathematika wafunda unanamhla. Mhlawumbi kwixesha elizayo, izicelo zayo ziya kuba ezinkulu.

Imvelaphi nezimaphambili ezingundoqo

Imbali ukuvela nophuhliso kwitrigonometri enze ngaphezu kwekhulu. Ukuqaliswa iikhonsepthi kuba sisiseko eli candelo yemathematika, naye akazange lolokwexeshana.

Ngoko ke, ingcamango "isono" unembali ende kakhulu. Ukuphawulwa seziqingatha ezahlukeneyo ukuzalana oonxantathu nezangqa zifumaneka nkqu kwimisebenzi zenzululwazi, niyathandana ukususela BC kwinkulungwane III. Imisebenzi zabaphengululi emikhulu amandulo ezifana Euclid, Archimedes, of ePerga, sele ziqulathe isifundo sokuqala ezi wobudlelwane. izinto ezintsha safuna utshintsho oluthile terminological. Ngenxa yoko, i-Indiya Isazinzulu Aryabhata unika Isingqi igama "Jiva", elithetha "usinga". Xa iitekisi Arab zezibalo eziguqulelwe kwisiLatin, igama kufuphi indawo yi lixabiso elinebaxiweyo (m. E. "Bend").

Kwabonakala Igama elithi "cosine" kakhulu kamva. Eli binzana segama ibinzana Latin "sine eyongezelelweyo '.

tangents Nesihlo ezinxulumene ne zokucazulula ingxaki yokufumanisa ubude besithunzi. Igama elithi "ilayini ezibambanayo kodwa azikweli" saqaliswa sezibalo Arab kwinkulungwane X Abu al-Wafa, inxalenye yezintlu yokuqala ukujonga ilayini ezibambanayo kodwa azikweli kunye elinekona ezisibhozo. Kodwa oosonzululwazi yaseYurophu wayengazi ngale mpumelelo. yezibalo German kunye ngeenkwenkwezi Regimontan rediscovers la magama ngo-1467 Ubungqina tanjenti theorem - ngetyala lakhe. A waguqulela elide njengoko 'achukumisayo ".