Te Whakamāramatanga o te Porowhita
Ko te porowhita tētahi o ngā āhua ā-ira tino taketake, ā, kua maumahara te tangata mai anō i ngā wā onamata. I roto i te pāngarau, ko te porowhita te huinga o ngā pūwāhi katoa i roto i te papa e ōrite ana te tawhiti mai i tētahi pūwāhi pumau. Ka kiia tēnei pūwāhi pumau ko te pokapū o te porowhita, ā, ko te tawhiti mai i te pokapū ki tētahi pūwāhi i runga i te porowhita ka kiia ko te radius.
1. Te Whakamāramatanga o te Porowhita
Hei mārama pono ki te tikanga o te porowhita, me titiro tātou ki ōna huānga:
– Te Pokapū o te Porowhita: He pūwāhi pumau e ōrite ana te tawhiti o ngā pūwāhi katoa o te porowhita mai i reira.
– Pūtoro (r): Te tawhiti mai i waenganui o te porowhita ki tētahi pūwāhi i runga i te porowhita.
– Te whānui (d): Ko te tawhiti roa rawa atu i waenganui i ngā pūwāhi e rua i runga i tētahi porowhita e tika ana mā waenganui. Ko te whānui e rua te rahi o te pūtoro, ka taea rānei te tuhi i roto i te pāngarau ko \( d = 2r \).
2. Ngā Āhuatanga o ngā Porowhita
He āhuatanga whakamere, ahurei hoki ō ngā porowhita:
– He rite te roa o ngā rādius katoa o te porowhita.
– He āhua ōrite te porowhita huri noa i tōna pokapū.
– Mā ia diameter ka wehea te porowhita kia rua ngā wāhanga ōrite.
– He kōpiko kati te porowhita, kāore he tīmatanga, kāore hoki he mutunga.
3. Whārite Porowhita
I roto i te pūnaha taunga Cartesian, ko te porowhita kei te pūwāhi \((h, k)\) me te radius \(r\) te pokapū, ā, koia te whārite paerewa:
\[ (x – h)^2 + (y – k)^2 = r^2 \]
Mena kei te pūtake te pokapū o te porowhita \((0,0)\), ka māmā ake te whārite:
\[ x^2 + y^2 = r^2 \]
4. Te Porowhita me te Horahanga o te Porowhita
Ko te tatau i te porowhita me te horahanga o te porowhita he mahi matua e rua e mahia pinepine ana i roto i te āhuahanga.
– Te Porowhita o te Porowhita: Ko te porowhita o te porowhita ko te roa o ngā taha o waho katoa o te porowhita. Ko te tātai mō te porowhita o te porowhita ko:
\[ K = 2\pi r \]
Ko te \( \pi \) (pi) he pūmau pāngarau e tata ana ki te 3,14159.
– Te horahanga o te porowhita: Ko te horahanga o te porowhita ko te wāhi e nohoia ana e te porowhita i roto i te papa. Ko te tātai mō te horahanga o te porowhita ko:
\[ L = \pi r^2 \]
5. Te Hītori me te Hiranga o ngā Porowhita
He mea whakamīharo ngā porowhita, ehara i te mea i roto i te pāngarau anake, engari i roto hoki i te hītori me te ahurea o te tangata. He maha ngā wā ka kitea ngā porowhita i roto i te taiao, pērā i te rā, te marama, me te maha atu o ngā mea o te rangi. I roto i te ahurea o te tangata, he maha ngā wā ka honoa ngā porowhita ki te tino pai me te katoa.
– Te Tātaritanga whetū me ngā Maramataka: Ko ngā nekehanga o ngā aorangi me ngā whetū i te wāhi e whai ana i ngā ara porowhita, tata porowhita rānei. I te nuinga o te wā, ko ngā maramataka onamata i ahu mai i ngā huringa o te marama me te rā.
– Hoahoa Whare me ngā Toi: E whakamahia ana ngā porowhita i roto i ngā hanganga hoahoa maha, pērā i ngā tuanui me ngā pourewa, tae atu ki ngā hoahoa toi mai i ngā mandala ki ngā wira.
6. Ngā Porowhita i te Oranga o Ia Rā
He maha anō ngā whakamahinga whai hua o ngā porowhita i roto i te oranga o ia rā:
– Ngā Wira me ngā Taputapu: Ko te wira tētahi o ngā mea tino hanga a te tangata, me tōna āhua porowhita. Ka āwhina ngā taputapu ki te tuku mana mā te nekehanga hurihuri.
– Ngā karaka: He maha ngā porowhita e whakaatuhia ai te wā, pērā i ngā karaka pakitara me ngā wati ringaringa.
– Ngā Hākinakina: I roto i ngā momo hākinakina, ka whakamahia ngā porowhita ki ngā papa tākaro, ki ngā pōro, me ētahi atu taputapu hākinakina.
7. Ngā Porowhita i roto i te Pāngarau Matatau
I roto i ngā pāngarau uaua ake, he mea nui te mahi a ngā porowhita i roto i ngā peka pūtaiao maha.
– Āhuahanga Ūkurīniana: He mea taketake te porowhita e āwhina ana ki te hanga i ngā ariā āhanga maha.
– Tātari Uaua: I roto i te pāngarau uaua, ko te porowhita te huinga o ngā pūwāhi katoa i tētahi tawhiti kua whakaritea mai i te pokapū i roto i te papa matatini.
– Ariā Tau: Ko ētahi raruraru o te ariā tau ko te kimi i ngā pūwāhi i runga i tētahi porowhita he āhuatanga motuhake tōna.
8. Ngā Porowhita me Ētahi Atu Piko Porowhita
He tauira te porowhita o te kōpiko porowhita, engari he rite anō ngā kōpiko, pērā i te porowhita. Ko te porowhita he huinga pūwāhi e pumau ana te tapeke o ō rātou tawhiti mai i ngā pūwāhi pumau e rua (ngā arotahi). Ka taea te whakaaro he porowhita he take motuhake o te porowhita e tūtaki ai ngā arotahi e rua ki te pūwāhi kotahi, te pokapū.
9. Ngā Kaipāngarau me te Rangahau mō ngā Porowhita
He maha ngā tohunga pāngarau puta noa i te hītori kua ako i ngā porowhita, ā, kua whai wāhi mai ki tō tātou mōhiotanga ki tēnei āhua. Hei tauira, he tohunga pāngarau Kariki a Archimedes, he maha ngā takoha nui i tukuna e ia, tae atu ki te whakatau tata i te uara o te pi me te tino tika.
I whai wāhi atu hoki a Pierre-Simon Laplace, he tohunga pāngarau, he tohunga whetū Wīwī, ki te ako i ngā porowhita i roto i te horopaki o te nekehanga aorangi me te ariā tūponotanga.
10. Hangarau me ngā Taupānga Hou
I tēnei ao hou, kua kitea ngā whakamahinga hangarau maha mō te ariā o ngā porowhita. Hei tauira, i roto i ngā whakairoiro rorohiko, ka whakamahia ngā porowhita hei hoahoa i ngā atanga kaiwhakamahi me ngā kēmu. I roto i te miihini, ka whakamahia ngā porowhita hei hoahoa i ngā wāhanga hiato e hiahia ana kia maeneene te hurihanga, pērā i ngā peera me ngā tuku.
He maha hoki ngā porowhita e whakamahia ana e ngā rauropi hou mō te mōhio ki ngā tauira me te tātari whakaahua hei kimi me te mōhio ki ngā āhua i roto i ngā whakaahua matihiko. Hei tāpiri, i roto i ngā whakawhitiwhiti kōrero ahokore, ka whakamahia te ariā porowhita i roto i te hoahoa pūihi me te tohatoha tohu.
11. Mātauranga me ngā Porowhita
I roto i te mātauranga, ka tīmata te ako i ngā porowhita i te tamarikitanga. Mā te whakauru i te ariā o ngā porowhita i te kura tuatahi ka āwhina i te hanga i tētahi turanga pakari mō te āhuahanga me te pāngarau whānui. I a ngā ākonga e neke ana ki te mātauranga teitei, ka tūtaki rātou ki ngā porowhita i roto i ngā kaupapa uaua maha, pērā i te tātaitai me te āhuahanga tātari.
Whakamutunga
He āhua māmā noa te porowhita, engari he tino whai rawa ngā āhuatanga me ngā whakamahinga. Mai i tōna whakamāramatanga taketake ki ngā whārite pāngarau, mai i te hoahoanga ki ngā hangarau hou, he mahi nui tā ngā porowhita i roto i ngā āhuatanga maha o te ao. Mā te mārama ki ngā porowhita, ehara i te mea ka āwhina noa i te whakaoti rapanga pāngarau, engari ka whakatuwhera hoki i ngā māramatanga ki te ataahua me te tino pai o te taiao me te hangarau.
