History of trigonometry: fitowan da kuma ci gaban

Trigonometry tarihi ne inextricably nasaba da ilmin taurari, domin shi ne ya hadu da kalubale na wannan zamanin da kimiyya, da masana kimiyya ya fara gano dangantakar daban-daban canji a cikin alwatika.

Don kwanan wata, trigonometry ne Micro-lissafi, nazarin dangantaka tsakanin dabi'u na kusassari da tsawo daga cikin bangarorin da triangles, kazalika da tafiyad da bincike na algebraic sunayen trigonometric ayyuka.

Kalmar "trigonometry"

A lokaci, wanda ya ba da sunan ga wannan sashe na lissafi, aka fara samo a cikin suna daga cikin littafin ya wallafa da Jamusanci lissafi Pitiskusa a 1505. The kalmar "trigonometry" ne na Greek asali kuma yana nufin "don auna alwatika." Don zama mafi daidai, shi ne ba na zahiri girma na wannan adadi, amma game da yanke shawara, da cewa shi ne, tabbatas da dabi'u na ta ba a sani ba abubuwa anfani da aka sani.

Janar bayani game da trigonometry

Trigonometry tarihi ya fara fiye da biyu millennia da suka wuce. Da farko, da ya faru aka hade tare da bukatar sanin da kusassari na alwatika da al'amari rabo. A lokacin da gudanar da bincike ya bayyana cewa ilmin lissafi magana daga wadannan dangantakar bukatar gabatarwar musamman trigonometric ayyuka, wanda tun asali sanya fitar a matsayin mai lamba tebur.

Domin da yawa kawance sciences tare da lissafi impetus ga ci gaban trigonometry ne daidai tarihi. Origin kwana ji raka'a (digiri) hade da bincike da masana kimiyya na zamanin d Babila, ta dogara ne a kan sexagesimal tsarin da lissafi, wanda ya ba Yunƙurin zuwa na zamani da gidan goma, a yi amfani da yawa aiyuka Kimiyya.

An zaci cewa asali sun wanzu a matsayin wani ɓangare na trigonometry ilmin taurari. Sai ta fara da za a yi amfani da gine-gine. Kuma a kan lokaci, akwai da amfani da wannan kimiyya a fannoni daban daban na mutum aiki. Wannan, musamman, ilmin taurari, teku, da kuma iska kewayawa, acoustics, kimiyyan gani da hasken wuta, Electronics, gine da sauransu.

Trigonometry a farkon ƙarni

Shiryar da kimiyya data on tsira sauran kaya, da masu bincike ƙarasa da cewa tarihi na zargin trigonometry ake dangantawa da aikin Greek falakin Hipparchus, wanda da farko tunani a kan gano hanyoyin da za a warware triangles (siffar zobe). Ayyukansa kasance a cikin 2nd karni BC.

Shi ne kuma daya daga cikin mafi muhimmanci nasarorin da cewa lokaci ne domin sanin da rabo daga kafafu da kuma hypotenuse a dama alwatika wanda daga baya ya zama da aka sani da Pythagorean Theorem.

A tarihin ci gaban trigonometry a zamanin tsohuwar Girka ake dangantawa da sunan falakin Talomi - marubucin da geocentric tsarin na duniya cewa rinjaye kafin samman.

Greek Masana ilmin ba da aka sani ba tare da, cosine da tangent. Su yi amfani da allunan sami darajar da tsirkiya daga cikin da'irar amfani da wani contractible baka. A raka'a ji sun tsirkiya digiri, minti da sakan. Daya mataki ya daidaita sixtieth rabo radius.

Har ila yau, nazarin da tsoho Helenawa ciyar da ci gaban siffar zobe trigonometry. A musamman, Euclid a cikin "Abubuwa" Theorem take kaiwa a kan regularities rabo girma na bukukuwa na daban-daban diameters. Ayyukansa a cikin wannan filin sun zama irin turu ga ci gaban more kuma m yankunan na ilimi. Wannan, musamman, da fasaha na astronomical kida, ka'idar taswirar tsinkaya, wani sarari suKe daidaita tsarin, da sauransu. D.

Middle Ages: nazarin India masana kimiyya

Gagarumin ci gaba cimma na da India Masana ilmin. A mutuwa na zamanin d kimiyya a IV karni kai ga motsa a cikin ci gaban ilmin lissafi a India.

A tarihin na zargin trigonometry a matsayin mai raba sashe na ilmin lissafi bada fara a tsakiyar zamanai. Wannan lokacin da masana kimiyya maye gurbin da tsirkiya sinuses. Wannan samu yarda ya shiga cikin ayyukan game da nazarin tarnaƙi, kuma kusassari da wani hakki alwatika. Wancan ne, shi ne to farkon ware wani trigonometry daga ilmin taurari, zama wani reshe na lissafi.

A farko tebur na sines kasance a Aryabhata, su da aka gudanar a 3 ^of 4 ^na 5 ^a. Daga baya, akwai cikakken versions na alluna: musamman, Bhaskara jagoranci ta hanyar ba tare da tebur 1 ^on.

A farko musamman rubutun a kan trigonometry bayyana a X-XI karni. Its marubucin ya da tsakiyar Asiya masanin al-Biruni. A na da marubucin mafi zurfafa a cikin babban aikin "The Canon Mas'ud" (Littafi III), a trigonometry, wani tebur na sines (a increments na 15 ') da kuma wani tebur na tangents (a increments na 1 °).

A tarihin ci gaban trigonometry a Turai

Bayan da canja wurin da Arab treatises cikin Latin (XII-XIII c) mafi daga cikin ra'ayoyin da India da kuma Persian masana kimiyya da aka aro Turai kimiyya. A farko ambaci trigonometry kasance a cikin XII karni a Turai.

Kamar yadda masu bincike, da tarihi na trigonometry a Turai hade da sunan Banasare Richard na Wallingford, wanda shi ne marubucin da ayyukansu "Hudu daga cikin rubutun a kan kai tsaye da kuma inverted guitar." Wannan aikinsa shi ne na farko aikin da ake gaba ɗaya kishin trigonometry. By XV karni, mawallafa, da dama a cikin rubuce-rubucen ambaci trigonometric ayyuka.

History of trigonometry: New lokaci

A wannan zamanin, mafi masana kimiyya ya zama sane da m muhimmancin trigonometry ba kawai a cikin ilmin taurari da kuma ilmin bokanci, amma kuma a wasu yankunan na rayuwa. Shi ne, da farko, kuma farkon, manyan bindigogi, kimiyyan gani da hasken wuta da kuma kewayawa a kan dogon teku Voyages. Saboda haka, a cikin biyu da rabi na XVI karni, wannan batu ya sha'awar da yawa shahararren mutane na cewa lokaci, ciki har da Nikolaya Kopernika, Ioganna Keplera, Fransua Vieta. Samman dauki trigonometry surori da dama daga cikin rubutun "A cikin juyin da Samaniya duniyoyin" (1543). Daga baya, a cikin 60s na XVI karni, Retik - almajiri na samman - sakamakon a cikin "Tantancewar Part na ilmin taurari" pyatnadtsatiznachnye trigonometric Tables.

Fransua việt a "Ilmin Lissafi Canon" (1579) ya ba da wani cikakken da na din-din-din, ko da yake unproven, halayyar da lebur da kuma siffar zobe trigonometry. Kuma Albrecht Dürer shi ne daya ta hanyar wanda aka haife sinusoid.

Isa yabo Leonarda Eylera

Ba trigonometry zamani abun ciki da kuma irin bashi ya Leonarda Eylera. Ya rubutun "Gabatarwa ga bincike daga cikin iyaka" (1748) ya ƙunshi maanar kalmar "trigonometric ayyuka", wanda yake daidai da zamani. Saboda haka, masanin kimiyya ya iya sanin ko kishiya ayyuka. Amma dai ba duka.

Definition na trigonometric ayyuka a real line an sanya yiwu godiya ga bincike Euler ba kawai halatta korau malã'iku, amma kusassari Bole 360 °. Da shi shi ne karon farko da ya tabbatar da abin da ya rubuta cewa cosine da tangent wata dama kwana ne korau. Fadada daga dukan cosine kuma ba tare da shi ma da abin yabo daga wannan masanin kimiyya. A general ka'idar trigonometric jerin da kuma nazari na haduwa daga cikin jerin samu ba abubuwa na Euler ta gudanar da bincike. Duk da haka, aiki a kan bayani daga related matsaloli, ya sanya da yawa binciken a wannan filin. Yana da aka ta hanyar aikinsa aka ci gaba da tarihi na trigonometry. A takaice, a cikin rubuce-rubucen ya aikatã game da tambayoyi da kuma siffar zobe trigonometry.

Aikace-aikace trigonometry

Trigonometry ba related to aiyuka Kimiyya, a hakikanin rayuwar yau da kullum da shi yana da wuya amfani da ɗawainiya. Duk da haka, wannan al'amari ba ya rage da muhimmancin. Yana da muhimmanci sosai, misali, wata triangulation dabara da damar Masana ilmin to quite daidai auna da nisa zuwa taurari shiryayye kuma saka idanu kewayawa da tauraron dan adam da tsarin.

Har ila yau, trigonometry da ake amfani a kewayawa, music ka'idar, acoustics, kimiyyan gani da hasken wuta, bincike na kudi kasuwanni, Electronics, Yiwuwar ka'idar, statistics, ilmin halitta, magani (misali, a deciphering duban dan tayi duban dan tayi da kuma lissafta tomography), pharmaceutics, sunadarai, yawan ka'idar, seismology, meteorology , oceanography, cartography, yankunan da yawa na kimiyyar lissafi, topography da geodesy, gine-gine, imin sautin harshe, tattalin arziki, lantarki injiniya, inji aikin injiniya, kwamfuta graphics, crystallography, da sauransu. d. a tarihin trigonometry kuma da rawar a cikin nazarin enii halitta da kuma ilmin lissafi sciences ake yi karatu a wannan rana. Zai yiwu a nan gaba, da aikace-aikace zai zama ma fi girma.

Asalin da asali Concepts

A tarihin fitowan da kuma ci gaban trigonometry yana da fiye da karni. A gabatarwar da Concepts cewa samar da tushen wannan sashe na lissafi, kuma ya ba yanzu-yanzu.

Saboda haka, manufar "zunubi" yana da matukar dogon tarihi. Ambaton daban-daban segments na da dangantakar triangles da kuma da'irori da ake samu ko da a kimiyya ayyukansu, dating daga III karni BC. Waɗannan ayyukansu girma tsoho malamai kamar Euclid, Archimedes, Afaloni na Bariyata, riga dauke da farko nazarin wadannan dangantakar. New binciken bukaci da a wasu terminological canje-canje. Saboda haka, masanin kimiyyar Aryabhata bada tsirkiya sunan "Jiva", ma'ana "kibiya". Lokacin da Arab ilmin lissafi texts fassara a cikin Latin, da kalmar kusa maye gurbinsu da darajar ba tare da (m. E. "Bend").

The kalmar "cosine" ya bayyana da yawa daga baya. Wannan lokaci ne wani raguwa ga Latin kalmar "ƙarin ba tare".

Aukuwa tangents dangantawa da bidiyon dikodi matsalar kayyade tsawon daga cikin inuwa. Kalmar "tangent" da aka gabatar a cikin X karni Arab lissafi Abu al-Wafa, kashi na farko alluna domin sanin tangent da cotangent. Amma Turai masana kimiyya ba su san game da wadannan nasarori. Jamus lissafi da falakin Regimontan rediscovers wadannan matsalolin a 1467 Hujja tangent Theorem - misãlansa. A fassara da kalmar a matsayin "m".