Ture tauwehe aho. otinga o tapatoru

I roto i te ako o tapatoru i oke ai reira ko te pātai o te tātai i te hononga i waenganui i o ratou taha, me koki. I roto i te āhuahanga, te ture tauwehe o cosine homai me ngā sine te whakahoki oti tino ki te raruraru. Ko te nui o te rerekē kīanga pāngarau me tātai, ture, theorems me ture e pera e ki rerekē au maite faahiahia, poto, me te ngāwari whangai he herehere i roto ia ratou. Ko te ture tauwehe aho he tauira pirimia o te taua waihanga pāngarau. ina titiro koe i te tātai pāngarau katoa i kotahi Ki te ano i reira te mea he tetahi fifi i roto i te māramatanga o ngā ture pāngarau, te-waha tikanga me taka ki roto ki te wahi.

kitea te mōhiohio tuatahi e pā ana ki tenei ture tauwehe i roto i te puka o te taunakitanga o reira i roto i te anga o te mahi pāngarau o Nasir al-Din al-Tusi, teiti hoki ki te tekau ma toru te rau tau.

Tata ofi ki te hononga i waenganui i ngā taha me te koki i roto i tetahi tapatoru, he reira ia tapao e taea te tauwehe aho ki tatou whakaoti maha ngā raruraru pāngarau, me te āhuahanga o te ture kua kite i tono i roto i te whānuitanga o te mahi a te tangata mahi.

kī ia ture tauwehe sine e mo tetahi tapatoru āhuatanga e taha proportionality ki te ritenga atu pito o ngā sine. He he ano hoki te wāhanga tuarua o tenei ture tauwehe, kia rite ki te mea e rite ana te ōwehenga o tetahi taha o te tapatoru ritenga ki te aho o te koki ki te diameter o te porowhita whakaahuatia e pā ana ki te tapatoru i raro i whakaarohia.

I roto i te tātai rite titiro tenei faaiteraa

he / sina = b / sinB = c / sinC = 2R

He tohu o te ture tauwehe o ngā sine, i roto i putanga ngā o pukapuka e wātea ana i roto i te momo taonga o putanga.

Hei tauira, whakaaro tetahi o nga tohu, hoatu he whakamārama o te wahi tuatahi o te ture tauwehe. Ki te mahi i tenei, ka ui tatou i ki te whakamatau mateakí ki te kīanga sinC = c sina.

I roto i te tapatoru te noho ABC, hanga i te teitei BH. I roto i te kotahi ahua, ka takoto te H hangä ki runga ki te AC wāhanga, me te tahi atu i waho reira, i runga i te nui o te koki i te akitu o te tapatoru rānei. I roto i te take tuatahi, e taea te faaite i te teitei i roto i te koki me taha o te tapatoru rite BH = he sinC me BH = c Hinai, i te mea te taunakitanga e hiahiatia ana.

I roto i te take i reira te wāhi H ko waho o te wāhanga AC, e taea te tiki i te rongoā e whai ake nei:

= BH he sinC me VL = c hara (180-A) = c Hinai;

ranei = BH te hara (180-C) = a sinC ko VL = c sina.

Ka rite ki a koutou e taea te kite, ahakoa o kōwhiringa hoahoa, tae tatou i te hua e hiahiatia ana.

ka rapua e tatou te tohu o te wahi tuarua o te ture tauwehe ki te whakaahua i te porohita huri noa te tapatoru. Na roto i tetahi o nga altitudes tapatoru, hei tauira B, hanga he diameter porowhita. Kei te hono ana te pūwāhi hua i runga i te porohita D ki tetahi o te teitei o te tapatoru, kia tenei hei te pūwāhi A o te tapatoru.

Ki te whakaaro tatou i te tapatoru whiwhi Abd ko ABC, ka taea e tatou e kite i te taurite o koki C me D (e hāngai ratou i runga i te pewa taua). Na hoatu e te koki A he rite ki te iwa tekau nga nekehanga te hara D = c / 2R, hara C = c / 2R, QED ranei.

ture tauwehe sine Ko te tīmatanga mō te whānuitanga o ngā mahi rerekē ngā tūmomo. He attraction ngā tona tono mahi ko, rite he tokua ko o Ariā e taea ki te pā ana te uara o te taha tapatoru, hoariri koki me te pūtoro (diameter) o te porowhita circumscribed huri noa te tapatoru tatou. Ko te tapatahi me te wātea o te tātai whakaahua tenei faaiteraa pāngarau, whakaaetia ki te whakamahi i whānui tenei ture tauwehe ki te whakaoti i te raruraru i te tikanga o ngā whakaaro aunoa countable (ture kiriata, e kore te tepu, me pera atu.), Ko ara te taenga mai o te tangata mahi pūrere rorohiko kaha tuku iho hāngaitanga o tenei ture tauwehe.

e kore he wahi anake o te akoranga e hiahiatia ana o āhuahanga kura nui tenei ture tauwehe, engari i muri whakamahia i roto i te tahi mau mahi ahumahi.