Sine wave theorem no. mhinduro kubva zvokuridza

Kudzidza zvokuridza involuntarily pane mubvunzo kuti pakuverenga ukama pakati kumativi dzavo uye pamakona. In geometry, ari theorem no kuti cosines uye sines rinopa mhinduro kupfuura wakakwana kuti dambudziko. Zvakawanda zvakasiyana kwemasvomhu mashoko uye Masvomhu, mitemo, theorems uye mitemo yakadaro kuti akasiyana kunoshamisa kuwirirana, zvipfupi uye nyore mavari zvokudya musungwa. Sine theorem no inonyatsoratidza zvakadaro kwemasvomhu Pfungwa. Kana kutukwa dudziro uye asi pane mumwe chipingamupinyi mukunzwisisa kwemasvomhu mitemo, kana iwe tarira munhu akarongeka inonyatsoita zvose kamwechete rikawira munzvimbo.

mashoko yokutanga pamusoro theorem no ichi vaakawana muchimiro uchapupu mariri kuumbwa vari kwemasvomhu basa Nasir al-Din al-Tusi chaiko yevaKristu nematatu.

Achisvika pedyo ukama pakati kumativi uye pamakona chero Triangle, zvinokosha kuziva kuti Sine theorem no kunotibvumira matambudziko akawanda akarongeka, uye geometry mutemo anowana kushanda nenzira dzakasiyana-siyana hunobatsira basa nevanhu.

Iye sine wave theorem no inoti kuti chipi netriangle kunoratidzwa proportionality mativi kuti pakatarisana makona sines. Panewo chikamu theorem no ichi chechipiri, maererano izvo reshiyo upi divi Triangle chakatarisana Sine ari pakona akaenzana kuti dhayamita ari denderedzwa zvinorondedzerwa pamusoro Triangle pasi kukurukurwa.

In nzira yemaitiro aya sokunge

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

It ane uchapupu theorem no pakati sines, izvo mushanduro mabhuku zvinowanikwa akapfuma siyana mushanduro dzakasiyana-siyana.

Somuenzaniso, funga mumwe uchapupu, achipa utsanangurirwe chikamu theorem no wokutanga. Kuti aite izvi, chatichakumbira kuratidza kuvimbika kune mashoko ane sinC = C Sina.

Munzvimbo zvemasanga netriangle ABC, kuvaka kukwirira Mwari bh. Mune imwe musimboti, ari kuvaka H ucharara pasi chidimbu AC, uye mumwe kunze kwayo, zvichienderana kwakakura pamakona panguva vertices pakati zvokuridza. Muchiitiko chokutanga, kureba kungaratidzwa kuburikidza pamakona uye mativi Triangle sezvo Mwari bh = munhu sinC uye Mwari bh = d Sina, inova zvaida uchapupu.

Apo H-ndeyekuti kunze chidimbu AC, tinogona kuwana zvinotevera zvingaitwa:

Mwari bh = munhu sinC uye Kuchibhotla = C chivi (180-A) = b Sina;

kana Mwari bh = chivi (180-C) = uye sinC uye Kuchibhotla = b Sina.

Sezvaunogona kuona, zvisinei yokugadzirwa zvokusarudza tisvike panguva achida mugumisiro.

The uchapupu chikamu theorem no yechipiri kuchatibatsira zvinoda kutsanangura denderedzwa akapoteredza Triangle. Kuburikidza rimwe Triangle altitudes, somuenzaniso B, avake denderedzwa dhayamita. The zvichiguma pfungwa pamusoro denderedzwa D zvakabatana mumwe kukwirira, triangle, regai ichi kuva pfungwa A yacho Triangle.

Kana tikafunga kuti vakawana zvokuridza ABD uye ABC, tinogona kuona wakaenzana pamakona C uye D (vari kwakavakirwa chete chinhu chakakombama). Uye akapiwa kuti pakona A akaenzana makumi madhigirii chivi D = c / 2R, kana chivi C = c / 2R, QED.

Sine theorem no ndiyo pokutangira zvakawanda mabasa akasiyana. A chaiyo kukwezvwa kwayo kushanda, ave corollary pakati Theorem tinokwanisa kurondedzera kukosha Triangle mativi, anoshorana pamakona uye nharaunda (dhayamita) ane denderedzwa circumscribed kumativi Triangle. The nyore uye Kuwanikwa payakavakirwa achirondedzera ichi kwemasvomhu mashoko, akabvumira kuti zvikuru kushandisa theorem no ichi kugadzirisa matambudziko achishandisa siyana zvemaziso mano countable (yemasiraidhi mitemo, matafura, uye nezvimwewo.), Asi kunyange kusvika basa munhu simba kadambari mano haina kutura chakakoshera theorem no ichi.

theorem no ichi hachisi chete chikamu zvaida weboka chesekondari geometry, asi gare gare kushandiswa mune dzimwe maindasitiri tsika.