Ngā Wāhanga Kōnika Porowhita: Te Tikanga, Ngā Whakamahinga, me te Hiranga i roto i te Oranga o Ia Rā
Pendahuluan
He ariā nui ngā wāhanga kōniko i roto i te pāngarau me te āhuahanga. E whā ngā momo matua o ngā wāhanga kōniko: ngā porowhita, ngā porowhita, ngā parabola, me ngā hyperbola. Ka arotahi tēnei tuhinga ki tētahi wāhanga kōniko whakamere me ngā tono maha o te ao tūturu: te porowhita. Ka whakamāramahia e mātou he aha te porowhita, ōna āhuatanga, me ōna tono me tōna hiranga i roto i ngā momo mara.
Te Whakamāramatanga me ngā Āhuatanga o ngā Porowhita
He wāhanga kōniko te porowhita e taea te whakaahua hei huinga pūwāhi i roto i te papa, e rite tonu ana te tapeke o ngā tawhiti mai i ngā pūwāhi pumau e rua, e kiia nei ko ngā arotahi. I roto i te pūnaha taunga Cartesian, ka taea te tautuhi i te porowhita mā te whārite:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
ko \(a\) me \(b\) ngā roa o te tuaka haurua-matua me te tuaka haurua-iti o te porowhita.
Ngā Āhuatanga o ngā Porowhita
Ko ētahi o ngā āhuatanga nui o ngā porowhita ko:
1. Tuaka Matua me te Tuaka Iti:
– Ko te tuaka matua te rārangi e hono ana i ngā pūwāhi tawhiti rawa e rua i runga i te porowhita; ko tōna roa he 2a.
– Ko te tuaka iti he rārangi e hono ana i ngā pūwāhi tata e rua i runga i te porowhita; ko tōna roa ko 2b.
2. Arotahi:
– E rua ngā arotahi o te porowhita kei runga i te tuaka matua, ā, ka taea te kimi i te tūranga o te pūwāhi arotahi mā te whakamahi i te whārite \(c^2 = a^2 – b^2\), ko \(c\) te tawhiti mai i te pokapū o te porowhita ki tētahi o ngā arotahi.
3. Te āhua rerekē:
– Ko te āhua rerekē o te porowhita he ine i te porowhita, ā, ka tatauhia ko \(e = \frac{c}{a}\). Kei waenganui i te 0 me te 1 tonu te āhua rerekē o te porowhita. Mena \(e = 0\), he porowhita te porowhita.
4. Te horahanga o te porowhita:
– Ka taea te tatau i te horahanga o tētahi porowhita mā te whakamahi i te tātai \( \pi \times a \times b \).
Ehara i te mea he āhua ā-ira ataahua noa te porowhita ki te titiro atu, engari he maha hoki ōna whakamahinga mahi tino whai tikanga.
Ngā Whakamahinga o ngā Porowhita i te Oranga o Ia Rā
Te Tātaritanga whetū
Ko tētahi o ngā whakamahinga rongonui o ngā porowhita ko te ao whetū. E whakamārama ana ngā ture a Kepler mō te nekehanga o ngā aorangi he porowhita ngā porowhita o ngā aorangi e karapoti ana i te Rā, ko te Rā te arotahi kotahi. Ko tēnei ture tētahi o ngā ture e toru a Kepler e whakaahua ana i te nekehanga o ngā tinana o te rangi. Mā te mārama ki ngā porowhita porowhita, ka taea e ngā kaipūtaiao te matapae i ngā tūranga o ngā aorangi, ngā wheturangi, me ngā asteroids me te tino tika.
Hangarau Whakawhitiwhiti Kōrero
He mea nui anō hoki ngā tono a ngā porowhita i roto i te hangarau whakawhitiwhiti kōrero. Ko ngā pūihi parabolic, e whakamahia ana hei whiwhi tohu pouaka whakaata, amiorangi rānei, ka whakamahi i ngā whakaata porowhita hei arotahi i te tohu ki te kaiwhiwhi. Mā tēnei ka taea e te pūihi te hopu i ngā tohu ngoikore me te whiwhi i aua tohu me te kounga pai ake. Ka whakamahia anō hoki tēnei ariā porowhita i roto i ētahi atu hoahoa pūihi e hiahia ana kia arotahi ki tētahi pūwāhi motuhake.
tuku kōrero
I roto i ngā mahi whatu, ka whakamahia ngā karāhe porowhita hei arotahi i te mārama me te whakaiti i ngā hapa whatu. He mea nui tēnei i roto i te hoahoa o ngā karu tiro, ngā karu hiko, me ētahi atu taputapu whatu. Ka whakamahia hoki ngā whakaata porowhita hei arotahi i ngā hihi mārama, i ētahi atu ngaru hiko rānei ki tētahi pūwāhi arotahi motuhake.
Hoahoanga me te Toi
E whakamahia ana ngā porowhita i roto i te hoahoa whare hei waihanga i ngā wāhi ataahua, whai hua hoki. Hei tauira, ko te porowhita, e whakamahia pinepine ana i roto i ngā hoahoa o te colosseum, o ngā papa tākaro rānei. Ka whakaratohia e ngā porowhita he āhua e tata atu ana ki te porowhita engari he nui ake te ngāwari o te hoahoa. I roto i te toi, ka whakamahia ngā porowhita hei tāpiri i te hihiri me te nekehanga ki ngā mahi toi pēnei i ngā peita, ngā whakairo, me ngā hoahoa whakairoiro.
I roto i te oranga o ia rā
He maha ngā āhuatanga o te oranga o ia rā e kitea ana ngā ara porowhita, kāore pea tātou e mōhio. Hei tauira, ko ngā ara oma i roto i ngā papa tākaro he porowhita te tikanga kia rite te tawhiti puta noa i ngā ara rerekē. Mā tēnei āhua porowhita ka whakaratohia he haumaru me te whakamarie mō ngā kai-oma.
Te Hiranga o te Pāngarau me te Ariā Tau
He mea nui anō hoki ngā porowhita i roto i te ariā tau me te pāngarau. E whakamahia ana te ariā o te porowhita i roto i te rangahau i ngā raruraru pihi porowhita i roto i te ariā tau, koinei tētahi o ngā kaupapa rangahau tino hohe me te nui i roto i te pāngarau hou. He tono anō hoki ngā pihi porowhita i roto i te whakamunatanga, inā koa i roto i ngā rauropi whakamunatanga kī-tūmatanui e kiia nei ko te whakamunatanga pihi porowhita (ECC). Ko te ECC tētahi o ngā tikanga whakamunatanga tino haumaru me te tino whai hua e whakamahia ana i ēnei rā.
Whakamutunga
He āhua ā-ira te porowhita, he maha ngā āhuatanga me ngā whakamahinga. Mai i te whetū arorangi ki te hangarau whakawhitiwhiti kōrero, te tirohanga, te hoahoanga, me te toi, he mahi nui tā te porowhita. Mā te mārama ki ngā āhuatanga o ngā porowhita, ehara i te mea ka kitea he māramatanga hohonu ake ki te ao pāngarau, engari ka taea hoki e tātou te waihanga me te arotau i te hangarau me ngā hoahoa i roto i te oranga o ia rā. Ko tōna hiranga ki te ariā tau me te whakamunatanga e whakanui ana i te hiranga o te porowhita i roto i te whanaketanga o te pūtaiao me te hangarau hou.
Ko ngā porowhita, me ō rātou uauatanga me ō rātou ataahua katoa, ehara i te mea ka tāpiri noa i tētahi taha hou ki tō tātou māramatanga pāngarau engari ka whakarato hoki i ngā otinga whai hua mō ngā raruraru o te ao tūturu e pā ana ki a tātou. Mā te haere tonu ki te tūhura me te mārama ki ngā porowhita, ka whakatuwherahia e tātou he maha atu ngā whai wāhitanga mō te auahatanga me te ahunga whakamua i roto i ngā momo mara.
