Te Pānga-toru: Ngā Ariā, Ngā Hītori, me Ngā Whakamahinga i roto i te Oranga o Ia Rā
Pendahuluan
He peka hou o te pāngarau te ine whārite, ā, he mea nui tana mahi i roto i ngā momo mara pūtaiao me te hangarau. E ako ana i ngā whanaungatanga i waenga i ngā koki me ngā roa taha i roto i ngā tapatoru. He wāhanga nui o te pāngarau, he whānui ngā tono a te ine whārite, mai i te whetū me te hangarau ā-iwi ki te whakatere me te hangarau mōhiohio. E whakamārama ana tēnei tuhinga i ngā ariā taketake o te ine whārite, tōna whanaketanga hītori, me ōna tono i roto i te oranga o ia rā.
Ngā Ariā Taketake o te Pāngatoru
I ahu mai te kupu trigonometry i ngā kupu Kariki e rua: "trigonon," arā, ko ngā koki e toru, me "metron," arā, ko te ine. Nō reira, ko te tikanga o te trigonometry ko 'te ine i ngā koki e toru'.
Ngā Mahi Pāngatoru
Kei te ngako o te ine whārite ngā mahi ine whārite taketake: sine (sin), cosine (cos), me te tangent (tan). Ka tautuhia ēnei mahi i roto i te horopaki o te tapatoru matau, arā:
– Ko te sine (sin) o te koki θ ko te ōwehenga i waenga i te roa o te taha whakarara o te koki me te roa o te hypotenuse.
– Ko te kōsina (cos) o te koki θ ko te ōwehenga i waenganui i te roa o te taha tata o te koki (e pātata ana) me te roa o te taha whakarara.
– Ko te tānga (tan) o te koki θ ko te ōwehenga i waenga i te roa o te taha whakarara o te koki me te roa o te taha tata o te koki.
Mō ngā koki neke atu i te 90 nekehanga, iti iho rānei i te 0 nekehanga, ka taea te tatau i ngā uara o te sin, cos, me te tan mā te whakamahi i te ariā o te porowhita waeine e whakamahia ai he porowhita me te radius waeine hei tautuhi i ngā mahi trigonometric.
Ngā Tuakiri Pātoru
Ko te tuakiri pākoki he whārite e whakamahi ana i ngā mahi pākoki e pono ana mō ngā koki katoa. Ko te tuakiri taketake rongonui ko te tuakiri Pythagorean:
\[ \sin^2\theta + \cos^2\theta = 1 \]
Ko ētahi atu tuakiri ko ngā tuakiri koki tāpiri me ngā panonitanga takirua:
\[ \sin(\alpha \pm \beta) = \sin\alpha \cos\beta \pm \cos\alpha \sin\beta \]
\[ \cos(\alpha \pm \beta) = \cos\alpha \cos\beta \mp \sin\alpha \sin\beta \]
Hītori o te Whanaketanga o te Pānga-toru
I tīmata te whanaketanga o te ine pākoki i ngā iwi onamata, inā koa ngā ahurea o Īhipa, o Papurona, me Kariki.
Papurona me Ihipa
I whakawhanakehia e ngā Pāpurona me ngā Ihipiana o mua ētahi tikanga ine me te tatau, e kiia nei ko ngā tūāpapa o te ine whārite. I whakamahia e rātou ngā ripanga aho hei tatau i te roa o ngā taha o ngā tapatoru.
Ngā Wā Kariki Tawhito
I ahu mai tētahi takoha nui i te tohunga pāngarau Kariki a Hipparchus (tērā pea 190–120 BC), e mōhiotia ana ko te "Matua o te Ine Taurite." Nā Hipparchus i tito ngā ripanga ine taurite tuatahi, e āhei ai te tatau tika i ngā koki me ngā roa taha.
Ngā Tau Waenganui
I te wā o te Ihirama, i whakawhānui ake ngā kaipūtaiao pērā i a Al-Battani rāua ko Al-Khwarizmi i te ako i te ine whārite mā te tāpiri i ngā mahi ine whārite hou me te tatau i ngā ripanga ine whārite tika ake. I tēnei wā, i tino mōhiotia ngā mahi ine whārite sine me te cosine.
Wā Hou
I tutuki i ngā tohunga pāngarau pēnei i a Leonhard Euler me ētahi atu ngā whanaketanga nui o te ine whārite o ēnei rā. Hei tauira, nā Euler i whakauru te mahi taupū, ā, i whakatū he hononga hohonu i waenga i te ine whārite me te tātari matatini.
Ngā Whakamahinga o te Pāngatoru i roto i te Oranga o Ia Rā
Ehara i te mea he taputapu ariā noa iho te pākoki i roto i te pāngarau, engari he maha hoki ngā tono mahi a ia i roto i ngā mara maha.
Te Tātaritanga whetū
He taputapu nui te ine whārite i roto i te whetū arorangi, hei āwhina i ngā kaimātai arorangi ki te ine i te tawhiti i waenga i ngā whetū, ngā aorangi, me ētahi atu tinana o te rangi. Hei tauira, ka whakamahia e te tikanga parallax whetū te ine whārite taketake hei tatau i te tawhiti o te whetū tata rawa atu i te Ao.
Te Hangarau Ā-Iwi me te Hoahoa Whare
I roto i te hangarau ā-iwi me te hoahoanga, ka whakamahia te ine pākoki hei tatau i ngā pari, te kaha o te hanganga, me te hoahoa whare. Hei tauira, ka whakamahia hei whakatau i te roa o ngā taha me ngā koki o ngā piriti, o ngā whare teitei rānei.
Whakatere
Ka whakamahia e ngā heramana me ngā pailate te ine ine hei whakatau i tō rātou tūranga i te moana, i te rangi rānei. Mā te whakamahi i ngā taputapu pēnei i ngā ine ira me ngā kāpehu, ka taea e rātou te tatau i ngā taunga whenua i runga i te koki i waenganui i te pae tawhiti me ētahi tinana o te rangi.
Hangarau Mōhiohio me te Whakawhitiwhiti Kōrero
I te ao o te hangarau mōhiohio me te whakawhitiwhiti kōrero, he maha ngā wā ka tukatukahia ngā tohu matihiko mā te whakamahi i ngā ariā pātoru. Ko te tātari Fourier, he tikanga mō te whakatata i ngā mahi ā-wā me ngā tohu, e whakawhirinaki nui ana ki ngā mahi sine me te cosine.
Ngā rongoā
Ko ngā matawai pēnei i te CT scan me te MRI me whakamahi i te trigonometry hei hopu i ngā whakaahua toru-ahu. Mā tēnei ka taea e ngā tākuta te tiki i tētahi mahere mārama, tika hoki o te wāhanga tinana e tirotirohia ana.
Te Matawhenua me te Mahere Whenua
He āwhina anō hoki te ine whārite i te ruri whenua me te mahere whenua. Ka whakamahia e te matawhenua te ariā o te tapatoru, arā, ko ngā wāhi me ngā tawhiti i runga i te mata o te Ao ka tatauhia i runga i ngā inenga koki mai i tētahi pūwāhi pumau.
Te Katinga
Ko te ine ira-whārite tētahi o ngā peka tino nui o te pāngarau, ā, he kaha tōna noho ki te ao o ia rā me ngā hangarau hou. Ahakoa i ahu mai tōna pūtake i te ine ngāwari i ngā koki me ngā roa taha i roto i ngā tapatoru, kua hipa atu ōna tono i ngā rohe mahi hei tautoko matua i roto i ngā momo kaupapa pūtaiao. Mai i te whakawhanaketanga o ngā hanganga ki te tūhuratanga ātea, he tūāpapa nui tonu te ine ira-whārite i ngā āhuatanga katoa. Mā te mārama ki ōna ariā me āna tono taketake, ka kite tātou i te hiranga o tēnei pūtaiao ki te whakarei ake i te oranga o te tangata.
Daftar Pustaka
1. Boyer, Carl B. (1991). He Hītori o te Pāngarau. Wiley.
2. Merzbach, Uta C.; Boyer, Carl B. (2011). He Hītori o te Pāngarau.
3. Katz, Victor J. (1998). He Hītori o te Pāngarau: He Kupu Whakataki.
He kupu whakataki roa tēnei. Kei roto i tēnei tuhinga he tirohanga whānui mō te ine whārite, mai i ngā kaupapa matua ki ōna whakamahinga i roto i te oranga o ia rā. Ka taea e koe te tāpiri atu i ētahi atu taipitopito, i ētahi tauira rānei mēnā e hiahiatia ana.
