Mōʻaukala o ka trigonometry: muli a me ka ulu ana

Trigonometry mōʻaukala ua inextricably ua hoʻopili i kilohōkū, no ka mea, mea, e hālāwai me ke kū'ē'ē 'ana o kēia' epekema kahiko, hoomaka ae la kānakaʻepekema, e makaikai i ka pilina o ka okoa aiaiiuo i loko o ka triangle.

I ka lā, trigonometry mea he anakahi iki-makemakika, këia i ka pilina ma waena o nā aiee o ka pana pua, a me ka lōʻihi o nāʻaoʻao o nā triangle mauna, e like me ka pono i kanaka me ka ai me ka Ikepili o algebraic identities o trigonometric hana.

Kaʻia "trigonometry"

Ke kau, i haawi inoa a hiki i keia pauku o ka makemakika, i mua i loaʻa i loko o ka inoa o ka puke no ka mea kākau ma ka Kelemānia mathematician Pitiskusa i ka 1505. Ka hua'ōlelo "trigonometry" mea o Helene kumu, a 'o ia hoʻi "e ana i kekahi triangle." Ia e oi kūlike loa, ia mea,ʻaʻole he literal Ana o keia huahelu, akā, e pili ana i kona hoʻoholo 'ana, i ka mea, i maopopo ai i nā loina o kona ike ole hehee wale hoʻohana' ana iʻikeʻia.

General 'ike e pili ana i trigonometry

Trigonometry mōʻaukala, hoomaka ae la oi ma mua o nā millennia aku nei. Initially, kona hanana i pili i ka pono, e hooholo i ka pana pua o ka triangle, a me ka lākiō hiʻohiʻona. I loko o ka noiʻi ka mea, ua hoʻomaka iholaʻo ia i ka makemakikaʻa o kēia mau hoahanau pono o ka hoʻokomo 'ia' ana o kūikawā trigonometric oihana, i i mua i mai like me ka laulā papaʻaina.

No ka mea, he nui Ally sciences makemakika impetus i ke kūpono 'ana o ke trigonometry i kaʻoi loa mōʻaukala. Me Kinohi makau huahelu huahelu (degere) pili me ka noiʻiʻepekema o kahiko Babulona, ua muli ma ka sexagesimal'ōnaehana o ka ho omaulia, a haawi ala i ka ke kālā no ka kekimala, hoʻohana 'ia i loko o na mea he nui e pili sciences.

Ua Ua ea ae ka hana i mua ola i kekahi hapa o ka trigonometry kilohōkū. A laila, ua hoomaka ia e ia i loko o kuhikuhipuʻuone. A ma manawa, ua i ka waiwai o kēia 'epekema i loko o kekahi mau kihapai o kanaka haʻawina. Kēia, ma ka nui, kilohōkū, kai a me ke ea hoʻokele, Acoustic, optics, uilaʻoe, kuhikuhipuʻuone a me na mea e ae.

Trigonometry ma ke kakahiaka nui kenekulia

Alakaʻi ma ka 'epekema ikepili ma luna o ke koena kea laa, ka noiʻi i manao ai, i ka mōʻaukala o ka muli o trigonometry ua pili i ka hana o ka Helene astronomer Hipparchus, ka mea mua manao i loaa ia mau aoao, e ke hoʻoponopono triangle mauna (spherical). Kana mau hana pili ana i ka 2nd kenekulia BC.

Ua mea no hoi kekahi o ka mea nui e piʻi like o ia manawa mea e hooholo i ka lākiō o na wawae, a me ka hypotenuse i loko o ka triangle akau a ma hope la ia mea e like me ka Pythagorean Theorem.

I ka moolelo o ka? Acaeoey o trigonometry i kahiko Greece ua pili i ka inoa o ka astronomer Ptolemy - i ka mea kākau o ka geocentric'ōnaehana o ko ke ao nei i lanakila mua Copernicus.

Ua i ike Greek astronomers sine, cosine a me ka tangent. Ka mea, hoʻohana papa, e imi i ka waiwai o ka chord o ka p ÷ ai ka hoʻohana 'ana i ka contractible piʻo. Nā naehana ana he chord degere, minuke a me kekona. Kekahi papahelu ua like ke kanaono kahahńnai hapa.

Nō hoʻi, haʻawina o ka mea kahiko Helene iā i ka hooulu ana o spherical trigonometry. I mau, Euclid ma o kona "hehee wale" theorem hiki aku ai ma luna o regularities ka lākiō. Ka leo o nā waihoʻoluʻu o ia wahi ka ho. ua lilo i ke ano o ka impulse i ke kūpono 'ana o ka nui a me ka pili mau mea o ka ike i kana mau hana ma keia kula. Keia, ma 'ana, ka' ike loea o ka Astronomical mau mea, i ka kumumanaʻo o ka palapala'āina nā wānana waiwai, ano lani i kahi kūlike o nenoaiu, a no laila, ma luna o. D.

Middle Ages: i ka hoʻopaʻa 'ana o Maunaʻepekema

Holomua loa ai kākou loaʻa medieval Indian astronomers. I ka make ana o ka 'epekema kahiko i loko o ka IV kenekulia alakai i ka' oni iki i loko o ka ulu ana o ka makemakika ma India.

I ka moolelo o ka muli o trigonometry like me ka pauku kaawale o ka makemakika kino i hoomaka ai i loko o ka Middle Ages. A i ka wa a kaʻepekema auou caiaiai ka chord sinuses. Kēia loaʻa 'ae e komo i kaʻoihana e pili ana i ka haʻawina aoao a me ka pana pua o ka triangle akau. Oia hoi, ka mea i laila ka hoʻomaka hookaawale ai i ka trigonometry mai kilohōkū, e lilo kekahi lālā o ka makemakika.

Ka mua papaʻaina o sines he ma Aryabhata, ua paʻa ka mea, i loko o 3 ^{o ka} 4 ^o 5 ^ma. Ma hope, ua piha wale nō o ka papa: ka nui, Bhaskara alakai ma sine papaaina 1 ^ma.

Ka mua hana kūikawā hoonoho ma trigonometryʻikeʻia ma ka X-XI kenekulia. Kona mea kākau i ka Central hawaiian haumāna AL-Biruni. A medieval mea kākau oi deepens i loko o kona papa hana "Ka Canon Masʻud" (Book III), ma ka trigonometry, ka papaʻaina o sines (i loko o xi o 15 ') a me ka papaʻaina o tangents (i loko o xi o 1 °).

I ka moolelo o ka? Acaeoey o trigonometry ma Europe

Ma hope iho o ka hoolilo ana o ¶ʻO'Araba hoonoho i loko o Roma (XII-XIII c) ka hapanui o nā manaʻo o ka Mauna a me Peresia kānakaʻepekema i aie Europa 'epekema. Ka mua iki o ka trigonometry e pili ana i ka XII kenekulia maʻEulopa.

E like me ka noiʻi, a me ka inoa o Pelekāne Rikeke o Wallingford, oia no ke kumu o ka hana i ka mōʻaukala o ka trigonometry ma Europe pili "Lau o ka hoonoho aku ma ka chords pololei a me ka hulu." I kana hana i ka hana mua i ka loa pau i ka trigonometry. Ma XV kenekulia, he nui kākau i loko o kā lākou mau palapala hōʻike i ka trigonometric hana.

Mōʻaukala o ka trigonometry: New manawa

I kēia manawa, ka hapanui epekema lilo ike o ka pilikia nui o ka trigonometry ole wale ma ka kilohōkū a me ka astrology, akā, i loko o nā wahi o ke ola. Kēia mea, mua o nā mea a pau, pū, optics a me ka hoʻokele ma luna o lōʻihi kai holo. No laila, i loko o ka lua o ka hapalua o ka XVI kenekulia, ua pili keia kumuhana nui koʻikoʻi kanaka o ia manawa, a me Nikolaya Kopernika, Ioganna Keplera, Fransua Vieta. Copernicus i trigonometry kekahi mau mokuna o kona hoonoho "Ma ka Hope o ka lani Spheres" (1543). Hope, ma na 60s o ka XVI kenekulia, Retik - he haumana no Copernicus - kūpono ai i loko o kona "'ōnohi Part o Lewanuʻu" pyatnadtsatiznachnye trigonometric papa.

Fransua Viet ma "makemakika Canon" (1579) haawi i ka ike piha, a kahua hoʻonohonohoʻana, naʻe unproven, ano o ka mea i lalo, a spherical trigonometry. A me Albrecht Dürer i ka kekahi ma ka mea i hanau sinusoid.

Nā pono Leonarda Eylera

Haawi trigonometry kēia maʻiʻo a me ke 'ano o ka aie i Leonarda Eylera. Kona hoonoho "Introduction i ka Ikepili o ka mea mana loa" (1748) kekahi i ka wehewehena o ka makahiki "trigonometric oihana", i mea equivalent i kaʻiʻo nō o kēia. Pela, ke nä känaka 'epekema ua hiki ke hooholo inverse oihana. Akā, i ka ole a pau.

Definition o trigonometric oihana ma luna o ka mea maoli laina i ua i hiki ai i ke aloha a hiki i ka noiʻi 'ana Euler ole wale ana io pana pua, akā, me ka pana pua B 360 °. Ua ua i ka manawa muaʻo ia i ho'āʻo ai ma kana mau palapala i ka cosine a me ka tangent o ka huina pono i io. ? Anoe? O holoʻokoʻa cosine a me ka sine ua hoi ka kānaka apau i mākaukau o keia nä känaka 'epekema. Ka General pähola 'o trigonometric puke a me ka hoʻopaʻa' ana o ka hoʻohui o ka hopena ua loaa i ole mea o Euler ka hoʻokolokolo 'ana i. Eia naʻe, e hana ana ma luna o ka pāʻoihana o nā pilikia, la oia i na mea he nui discoveries ma keia kahua. Ua Ua ma kana hana i hana mauʻia e ka mōʻaukala o ka trigonometry. Komo i loko o kona mau palapala ia i hana ia me na ninau a me spherical trigonometry.

noi trigonometry

Trigonometry mea,ʻaʻole i hōʻikeʻia ke noi sciences, ma ka makemake maʻamau o ke ola ka mea, ua kākaʻikahi i hoʻohana hana. Naʻe, i kēia mea, aole ia e hoemi kona nui. He mea nui, no ka laʻana, he triangulationʻano hana e leie aku astronomers eʻano pololei ana i ka mamao o ia hoku Manao iho, a kanaka hoʻoponopono hoʻokele ukali nenoai.

No hoi, ua hoʻohana 'trigonometry ma ka hoʻokele, mele kumumanaʻo, Acoustic, optics, Ka Ikepili o kālā aha kanaka, uilaʻoe, pahiki kumumanaʻo,' ikepili helu, kālaimeaola, lapaʻau (e like me deciphering ultrasound ultrasound a Me tomography), pharmaceutics, kemika, helu kumumanaʻo, seismology, meteorology , oceanography, cartography, no nā hana o ke kālaikūlohea, 'äina a me ka geodesy, kuhikuhipuʻuone, phonetics,? aneia iainiiaaiea, lolouila' enekinia, ma paʻi 'enekinia, kamepiula kiʻi, crystallography, a no laila, ma luna o. d. ka moolelo o ka trigonometry a me kona kūlana ma ke ao enii maoli a me ka makemakika sciences i aʻo ai i kēia lā. Paha i loko o ka wā e hiki mai, kona palapala noi, e ia i oi aku.

Nā kêia kanaka a ke kumu o manaÿo

I ka moolelo o ka muli a me ka hoʻomohala o trigonometry ua oi ma mua o ke kenekulia. I ka hoike ana o ka manaÿo e lilo i kumu o keia pauku o ka makemakika, i ua ole wā pōkole.

Ke'ī mai, i ka manaʻo o "hewa" i ka lōʻihi loa mōʻaukala. Olelo ai o Iosepa i ka Hoʻohana likeʻole o ka pilina o triangle mauna, a koʻikoʻi a hanohano i loaʻa, a hiki ma ka 'epekema hana, ka launa pū, mai ka III kenekulia BC. Na hana o ka naʻauao nui kahiko like Euclid, Archimedes, Apollonius o Perege, ua ka study mua o kēia mau hoahanau iloko olaila. New discoveries ninau mai la i kekahi terminological loli. Penei, ka Indian nä känaka 'epekema Aryabhata i haawi mai i ka chord inoa o "Jiva" penei ke ano, "bowstring". Ka wā ¶ʻO'Araba makemakika hāʻina o nā haʻawina unuhi 'ia i loko o Roma, i ka manawa kokoke auou caiaiai ia e ka cia sine (m. E. "lena").

Ka hua'ōlelo "cosine" ikea nui hope. Kēia manawa o ka hua h ÷ ailona no ka mea he Roma hopuna'ōlelo "hou sine".

Hanana tangents pili me ka ho omńkalakala i ka pilikia o ka hoomaopopo ana i ka lōʻihi o ka malu. Kaʻia "tangent" Ua hoʻolauna i loko o ka X kenekulia ¶ʻO'Araba mathematician Abu AL-Wafa, hapa o ka papa mua, e hooholo i ka tangent a me ka cotangent. Akā, Europaʻepekema i i ike e pili ana i kēia mau e piʻi like. German mathematician a me ka astronomer Regimontan rediscovers këia mau manaÿo ma ka 1467 e höʻoia 'tangent theorem - i kona ai. A unuhi i ka manawa e like me "pēnēia".