Te Tātai i te Porowhita Porowhita
He mea nui te mārama ki ngā āhuatanga o ngā āhua ā-irahiko o te pāngarau. I roto i ēnei āhua, he mea whakamiharo te porowhita nā tōna māmā me ōna pānga hohonu ki ngā momo wāhanga pāngarau me te pūtaiao. Ko tētahi o ngā āhuatanga nui o te porowhita ko tōna porowhita. I roto i tēnei tuhinga, ka ruku hohonu tātou ki te ariā o te porowhita, tōna hiranga, me ngā tikanga tatau.
He aha te Porowhita?
Ko te porowhita o te porowhita te tawhiti huri noa i te taha o te porowhita. He rite ki te taha o te polygon, engari, mō ngā porowhita, ka whakamahia e mātou te kupu porowhita. Ko te tikanga, ki te hikoi koe i te taha o te mara porowhita, ka rite te tawhiti i haerea e koe ki te porowhita o te porowhita.
Te Tātai Pāngarau mō te Porowhita
Hei tatau i te porowhita o tētahi porowhita, ka taea e koe te whakamahi i te tātai pāngarau:
\[ C = 2\pi r \]
kei hea:
– Ko te porowhita te \( C \).
– Ko te \( \pi \) (pi) he pūmau pāngarau e tata ana ki te 3.14159.
– Ko te \( r \) te pūtoro o te porowhita, arā, te tawhiti mai i waenganui o te porowhita ki tētahi pūwāhi i tōna taha.
Heoi anō, ki te mōhiotia te whānui \( d \) o te porowhita, ka taea te tuhi i te tātai penei:
\[ C = \pi d \]
nā te mea he rua te whānui o te whānui \( d \) i te pūtoro (\( d = 2r \)).
Te Mārama ki te Pi (π)
He tau whakawhiti te pūmau \( \pi \) (pi), arā, ehara i te pūtake o tētahi whārite pūrau kore-kore me ngā taunga whaitake. Ko te Pi he tata ki te 3.14159, engari he tau koretake, arā, ka mau tonu tōna whakaaturanga ira-ira me te kore e tāruarua. He mea nui te Pi i roto i te tatau i te porowhita nā te mea e tohu ana i te ōwehenga o te porowhita o te porowhita ki tōna whānui. Ahakoa te rahi o te porowhita, ka mau tonu tēnei ōwehenga.
Horopaki Hītori o te Porowhita me te Pi
Kua mōhiotia te ariā o te porowhita mai anō i ngā wā onamata. He huarahi ā ngā tohunga pāngarau o mua o ngā ahurea maha, tae atu ki ngā Pāpuroni me ngā Ihipiana, ki te whakatau tata i te porowhita o te porowhita. Hei tauira, i whakamahia e ngā Ihipiana o mua he uara o \( \pi \) tata ki te 3.1605, he tata ki te uara tuturu.
Nā Ākirīmete o Hirakahu, he tohunga pāngarau Kariki i noho i te tau 250 BC pea, tētahi o ngā whakatau tata tuatahi mō \( \pi \). I āta whakatau tata ia i \( \pi \) mā te tuhi me te tākai i ngā porowhita huri noa i tētahi porowhita me te tatau i ō rātou taha.
Ngā Tauira Tātaitanga Whaihua
Hei mārama ake ki te tatau i te porowhita, me titiro tātou ki ētahi tauira:
1. I runga i te Pūtoro:
Me kī he porowhita tā tātou me te radius o te 5 cm. Mā te whakamahi i te tātai:
\[ C = 2\pi r \]
\[ C = 2 \times \pi \times 5 \]
\[ C = 10\pi \]
Mā te whakamahi i te \( \pi \approx 3.14159 \):
\[ C \tata ki te 10 \whakareatia 3.14159 = 31.4159 \kuputuhi{ henimita} \]
2. I te mea kua hoatu te Diameter:
Mena he 10 cm te whānui o te porowhita, ka taea te tatau i te porowhita penei:
\[ C = \pi d \]
\[ C = \pi \whakareatia ki te 10 \]
\[ C = 10\pi \]
Anō, mā te whakamahi i te \( \pi \approx 3.14159 \):
\[ C \tata ki te 10 \whakareatia 3.14159 = 31.4159 \kuputuhi{ henimita} \]
Ka homai e ngā tikanga e rua te porowhita ōrite, e whakaatu ana i te whanaungatanga i waenga i te pūtoro me te diameter i roto i te tātai.
Ngā Whakamahinga o te Porowhita
Ehara i te mea he mahi mātauranga noa te tatau i te porowhita; he tono anō hoki mō te ao tūturu i roto i ngā mara maha:
1. Te Hangarau me te Hanga:
He maha ngā wā me tatau e ngā kaihangarau te porowhita ina hangaia ana ngā mea porowhita pēnei i ngā wira, ngā taputapu, me ngā paipa. He mea nui te whakatau i ngā rauemi e hiahiatia ana, me ngā ine tika hoki i roto i te tukanga hanga.
2. Te Tātaritanga whetū:
He maha ngā wā ka whakatauirahia ngā mea o te rangi pērā i ngā aorangi me ngā whetū hei porowhita, ā, mā te mārama ki ō rātou porowhita ka āwhina i te tatau i ō rātou porowhita me ngā tawhiti i te wāhi.
3. Te Oranga o Ia Rā:
Ko ngā mahi māmā noa iho pēnei i te ine i te awhi o te tauera tēpu porowhita, te whakatau rānei i te roa o te taiapa e hiahiatia ana hei karapoti i tētahi māra porowhita, me mārama ki te porowhita.
Ngā Wero i roto i te Tika
Ahakoa te nuinga o ngā tono taketake e whakamahi ana i te whakatau tata \( \pi \approx 3.14159 \), ko ngā tataunga tino tika ka hiahia pea ki ētahi atu mati o \( \pi \). Hei tauira, ka whakamahia pea e ngā miihini o NASA ngā tini mati o \( \pi \) i te wā e hoahoa ana i ngā waka rererangi hei whakarite kia tino tika ā rātou matapae mō ngā ara me ngā tawhiti.
whakarāpopototanga
Ko te tatau i te porowhita o te porowhita he pūkenga taketake i roto i te āhuahanga e pā ana ki ngā momo kaupapa pūtaiao me ngā kaupapa mahi. Ko te ngāwari o te \( C = 2\pi r \) me te \( C = \pi d \) e whakaatu ana i te ataahua o te pāngarau. Mā te mārama ki te ariā ka taea e te tangata te maioha ki ngā whanaungatanga uaua i waenga i ngā āhuatanga rerekē o ngā porowhita me ō rātou tono whānui.
Hei whakamutunga, ahakoa he tauira koe e whakaoti rapanga āhuahanga, he miihini e hoahoa ana i ngā mīhini, he tangata rānei e mahi ana i tētahi kaupapa kāinga DIY, he taputapu tino whai hua te mōhio ki te tatau i te porowhita o tētahi porowhita. Mā te mārama me te whakamahi i ngā mātāpono kua kōrerohia, ka taea e koe te whakatere me te whakaoti rapanga o te ao tūturu me te ngāwari me te tika.
