Ba tare da Theorem. bayani na triangles

A cikin nazarin triangles involuntarily akwai wata tambaya na kirga dangantaka tsakanin sãsanninsu, kuma kusassari. A lissafi, da Theorem na cosines da sines bada mafi cikakken amsar matsalar. Yawan daban-daban ilmin lissafi maganganu da dabarbari, dokokin, theorems da dokoki ne, irin abin da daban-daban m jituwa, rakaitacce da sauki don ciyar da wani fursuna, a gare su. Ba tare da Theorem ne Firayim misali na irin wannan ilmin lissafi halitta. Idan fi'ili fassarar kuma duk da haka akwai wani cikas a cikin fahimtar ilmin lissafi dokoki, lokacin da za ka duba a ilmin lissafi dabara, jimla guda shi ya faxa cikin wuri.

A farko bayanai game da wannan Theorem da aka samu a cikin nau'i na shaidar shi a cikin tsarin na ilmin lissafi aikin Nasir al-Din al-Dusi, dating mayar da goma sha uku karni.

Yayinda kusa da dangantaka tsakanin bangarorin da kusassari a wani alwatika, shi ne ya kamata a lura da cewa ba tare da Theorem yale mu mu magance da dama ilmin lissafi da matsaloli, da kuma lissafi na dokar sami aikace-aikace a cikin wani iri-iri m adam aiki.

Ta ba tare da Theorem ya furta cewa, domin kowane Bamuda shi ne halin da proportionality tarnaƙi ga m kusurwa sines. Akwai kuma kashi na biyu na wannan Theorem, bisa ga abin da rabo daga wani gefe na alwatika daura da ba tare da na kwana ne daidai ga diamita daga cikin da'irar da aka bayyana game da alwatika karkashin shawara.

A wani dabara wannan magana kama

a / Sina = b / sinB = c / sinC = 2R

Yana yana da hujja daga cikin Theorem na sines, wanda a daban-daban versions na litattafan samuwa a yi wani mai arziki iri-iri iri.

Alal misali, ka yi la'akari daya daga cikin shaidun, bada wani bayani na farko na Theorem. Don yin wannan, za mu tambaye su tabbatar da biyayya ga magana mai sinC = c Sina.

A wani sabani alwatika ABC, yi tsawo b. A daya embodiment, ba siffar H zai karya a kan sashi AC, da kuma sauran waje da shi, dangane da girma da kusassari a vertices na triangles. A farkon yanayin, da tsawo za a iya bayyana ta hanyar da kusassari da bangarorin na alwatika a matsayin b = wani sinC kuma b = c Sina, wanda shi ne ake buƙata shaida.

Lokacin da H-aya ne a waje na kashi AC, za mu iya samun mafita da wadannan:

B = wani sinC da VL = c zunubi (180-A) = c Sina.

ko b = zunubi (180-C) = kuma sinC da VL = c Sina.

Kamar yadda ka gani, ko da zane zabin, mun zo a da ake so sakamakon.

A hujja na biyu na Theorem za bukatar mu bayyana a da'irar a kusa da alwatika. Ta hanyar daya daga cikin alwatika altitudes, misali B, yi wata da'ira diamita. A sakamakon batu a cikin da'irar D an haɗa zuwa daya daga wani tsawo na alwatika, bari wannan ya zama batu A na alwatika.

Idan muka yi la'akari da samu triangles ABD da ABC, za mu iya ganin da daidaitakar kusassari C da D (suna bisa wannan baka). Kuma ba cewa kwana A daidai yake da casa'in digiri na zunubi D = c / 2R, ko kuwa wani zunubi C = c / 2R, QED.

Ba tare da Theorem ne masomin mai fadi da kewayon daban-daban ayyuka. A musamman janye ne ta m aikace-aikace, kamar yadda wani corollary na Theorem mu iya danganta da darajar da alwatika tarnaƙi, tsaurin kusassari da radius (diamita) na da'irar circumscribed a kusa da alwatika. A sauki da kuma samuwar dabara bayyana wannan ilmin lissafi magana, a yarda wa yadu amfani da wannan Theorem don warware matsalolin ta hanyar daban-daban inji na'urorin countable (nunin dokoki, alluna, da sauransu.), Amma ko da isowa daga cikin sabis mutum iko sarrafa kwamfuta na'urorin ne ba a saukar dacewar wannan Theorem.

Wannan Theorem ba wai kawai na bukata shakka daga makarantar sakandare lissafi, amma daga baya a yi amfani da wasu masana'antu yi.