Te Tapawhā me ōna Āhuatanga
Ko ngā tapawhā tētahi o ngā āhua tino taketake o te āhuahanga me te oranga o ia rā. He māmā noa iho engari he hohonu, e whakaatu ana i te huatau pāngarau me te ōritetanga e toro atu ana i tua atu i tōna āhua taketake. Ahakoa i runga i te papa tākaro, i roto rānei i ngā hoahoa whare, he mea nui ngā tapawhā ki ngā wāhi katoa. Ka rukuhia e tēnei tuhinga ngā āhuatanga o ngā tapawhā, ka tūhuratia ō rātou hiranga pāngarau, ō rātou whakamahinga, me ngā āhuatanga whakamere.
Te Tautuhi i tētahi Tapawhā
He tapawhā te tapawhā, arā, e whā ōna taha. Ko te mea e wehewehe ana i te tapawhā i ētahi atu tapawhā ko te roa ōrite o ngā taha e whā, ā, he koki tika tino tika ia koki, e 90 nekehanga te ine. Mā tēnei huinga o ngā taha roa ōrite me ngā koki ōrite ka whakawhiwhia te tapawhā ki tētahi huinga āhuatanga ahurei.
Ngā Āhuatanga Taketake
Ngā Taha me ngā Koki ōrite
Ko te āhuatanga matua o te tapawhā ko te ōrite o ngā taha e whā, arā, he ōrite te roa. Hei tāpiri, ko ia koki o roto he 90 nekehanga, ā, he tapatoru rite tonu. Nā te mea he ōrite ngā koki me ngā taha katoa, ka māmā ake tēnei āhuatanga i ngā tataunga me ngā taunakitanga maha i roto i te āhuahanga.
Ngakariko
Ko tētahi atu āhuatanga whakamīharo o ngā tapawhā ko ō rātou whakarara. E rua ngā whakarara o te tapawhā, ā, he āhuatanga whakamiharo ō rāua:
1. Roa Ōrite: He rite te roa o ngā hauroki o te tapawhā.
2. Poutū: Ka tūtaki ngā whakarara tetahi ki tetahi i te koki 90-tohu.
3. Wehewehea tetahi i tetahi: Ko te pūwāhi e tutaki ai ngā hauroki ka wehea ia hauroki kia rua ngā wāhanga ōrite.
4. Ngā Tuaka Āhuarite: He rārangi āhuarite ia whakarara, arā, ka taea te whakapiko i te tapawhā i ia whakarara hei hanga i ngā āhua ōrite e rua.
Ka taea te tatau i te roa o te whakarara mā te whakamahi i te ariā Pythagorean. Mō te tapawhā me te roa taha \(a\), ka hoatu te roa o te whakarara \(d\) e:
\[ d = a\sqrt{2} \]
Te horahanga me te taha
Mā te māmā o ngā tapawhā ka taea te tatau māmā i te horahanga me te paenga. Ka kitea te horahanga \(A\) o te tapawhā mā te tapawhā i te roa o tētahi o ōna taha:
\[ A = a^2 \]
Waihoki, ko te paenga \(P\) o te tapawhā ko te tapeke o te roa o ōna taha e whā:
\[ P = 4a \]
hangarite
He āhuatanga nui te ōrite o ngā tapawhā. He ōrite hurihuri, he ōrite whakaata hoki te tapawhā. Ka taea te huri mā te 90, 180, 270 nekehanga rānei, ā, he ōrite te āhua. E rite ana ēnei hurihanga ki ngā āhuatanga ōrite i roto i ngā momo mara, mai i te karaihe ki te toi me te hoahoa.
Ko te Kohinga Whakahaere
I roto i te papa taunga, ka taea te whakaatu ngāwari i ngā pito o te tapawhā mēnā ka mārama ki ōna āhuatanga. Mēnā kei te pūtake (0, 0) tētahi pito o te tapawhā, ā, ko te roa o te taha ko \(a\), ka taea e ngā pito te noho ki (0, 0), (a, 0), (a, a), me (0, a). Mā tēnei ka māmā ake te whakamahi i ngā panonitanga me te tatau i ngā tawhiti.
Taupānga Pāngarau
He whānuitia te whakamahinga o ngā tapawhā i roto i ngā momo wāhanga pāngarau nā te mea he māmā noa iho ō rātou āhuatanga.
Tuawaru
He mea nui te mōhio ki ngā tapawhā tino tika i roto i te pāngarau. Ko te whakataurite i ngā tapawhā, te whakaoti i te tapawhā, me te whakaoti whārite he maha ngā wā ka uru atu ki ngā āhuatanga o ngā tapawhā. Ko te rerekētanga o ngā tapawhā he āhua whakataurite noa:
\[ a^2 – b^2 = (a + b)(a – b) \]
Āhuahanga Ūkurīniana
I roto i te āhuahanga Euclidean, ko ngā tapawhā he āhua taketake mō te hanga me te whakaoti rapanga āhuahanga. Ka whakamahia ēnei hei tautuhi me te tūhura i ngā āhuatanga o ētahi atu āhuahanga, pērā i ngā tapawhā rite, ngā rhombuse, me ngā parallelgram.
Taekerau
I roto i te ine pākoki, ka āwhina ngā tapawhā ki te whakaatu me te whakaoti rapanga e pā ana ki ngā tapatoru tika. Ko te tapawhā kotahi, ina kotahi te waeine o ia taha, he mea nui ki te tautuhi i ngā mahi pākoki i runga i te papa Cartesian.
Nga tono mo te Ao-Tuturu
Whakaahua me te Hoahoa
He whānuitia ngā tapawhā i roto i ngā mahi hoahoa whare nā te mea he taurite te hanganga me te ātaahua. Ka whakarato i te pumau o te hanganga, ā, he maha ngā wā ka whakamahia i roto i ngā mahere papa, matapihi, taera, me ngā momo whakapaipai.
hangarau
I roto i te hangarau, inā koa ko te whakaahua matihiko, ko te pika tapawhā te waeine taketake o ngā whakaahua matihiko. Mā te whakamahi tonu i ngā pika tapawhā ka taurite, ka tika hoki te whakaputa whakaahua me ngā ataata.
Nga Taakaro me nga Puzzles
Ko ngā kēmu poari pēnei i te hēki, te tikēti, me te Scrabble e whakawhirinaki ana ki tētahi mata tapawhā hei whakarite i te tākaro. Mā ngā āhuatanga o te mata tapawhā ka whakarite i te tākaro tika me te taurite rautaki. Waihoki, ko ngā panga pēnei i te Sudoku me ngā panga kupu whakawhiti e whakamahi ana i ngā mata tapawhā hei whakarite i ngā huānga kia pūnaha.
Art
He maha ngā wā ka whakamahia e ngā kaitoi ngā tapawhā i roto i ā rātou tito hei tūhura i te ōritetanga, te taurite, me ngā whanaungatanga i waenga i ngā momo huānga. Ko te pūnaha mata, e whakamahi ana i ngā tapawhā, he mea nui i roto i ngā momo tikanga toi, tae atu ki te tuhi tirohanga me te hoahoa tauira.
Ngā Mea Pupuri
Ngā Tapawhā Makutu
Ko tētahi āhuatanga whakamere o ngā tapawhā ko te ariā o ngā tapawhā makutu. Ko te tapawhā makutu he whatunga tau me te āhuatanga he ōrite ngā tapeke o ngā tau i ia rarangi, pou, me te hauroki. Kua roa nei e miharo ana ngā tohunga pāngarau me ngā kaingākau ki ēnei, ā, he whakamahinga anō hoki kei roto i te hoahoa whakakotahi me te whakamunatanga.
Te Whakatapahia te Porowhita
Ko tētahi o ngā raruraru matarohia o te pāngarau ko te "whakatapawhā i te porowhita," arā, ko te hanga i tētahi tapawhā he rite te horahanga ki tētahi porowhita kua hoatu mā te whakamahi i tētahi maha iti noa o ngā hikoinga me te kāpehu me te taha tika. Kua whakamātauhia tēnei raruraru kāore e taea nā te mea kei tua atu i a π, engari kua akiakihia e ia te maha o ngā tūhuratanga pāngarau.
Ngā Toronga Ārai
I roto i te arapū, he mea nui te ariā o te tapawhā i ngā tau. Ko te whakawhānui i tēnei whakaaro ki ngā tau matatini ko te whakamahi i ngā tapawhā i roto i ngā whārite pūrau, he pānga ki ngā mara rerekē pērā i te ahupūngao, te hangarau, me te ariā tau.
Opaniraa
Ko te māmā o te tapawhā e huna ana i tōna hohonutanga me tōna whānui. Mā te mārama ki ngā āhuatanga o ngā tapawhā ka tuwhera he matapihi ki te ao whānui o te āhuahanga, te pāngarau, me ngā tono i te ao tūturu. Mai i te hoahoanga ki ngā kēmu, he mea nui ngā āhuatanga o te tapawhā. Nā ōna āhuatanga āhuahanga, te hiranga pāngarau, me ngā tono mahi, ka waiho ngā tapawhā hei kaupapa ako me te maioha e kore e mutu. Ehara i te mea he āhua noa ngā tapawhā; he kuaha ki te mārama ki ngā ariā pāngarau whānui me ngā pūnaha o te ao tūturu.
