Ngā Tauwehenga Pāngarau i roto i ngā Piramiti: He Arotake i te Pāngarau me te Hanga Whare o Mua
Ko ngā piramita o Īhipa, inā koa te Piramita Nui o Kiza, kua roa nei hei tohu mō te pūkenga hanga tangata, ā, he mea ngaro kāore anō kia whakatauhia. Ehara i te mea he mea whakamiharo noa iho te rahi me te tika o ēnei hanganga, engari he nui hoki ngā raraunga e tukuna ana e ngā tohunga pāngarau, inā koa i roto i te whakamahinga o te ine whārite. E tirotirohia ana e tēnei tuhinga te whakamahinga o ngā tikanga me ngā ariā ine whārite i roto i te hoahoa o ngā piramita o Īhipa, me te hiranga o ngā ōwehenga ine whārite ki te mārama ki tēnei hangarau hanga tawhito.
1. He Hītori Poto mō ngā Piramiti o Īhipa
Ko ngā piramita o Īhipa he hanganga whakahirahira i hangaia hei urupā mō ngā Parao me ngā kuīni i roto i te whakapono o Īhipa onamata mō te ao i muri i te matenga. Ko te piramita tawhito rawa atu e mōhiotia ana ko te piramita o Djoser i Saqqara, i hangaia i te wā o te Tuatoru o ngā Whare Ariki e Imhotep, te kaihoahoa rongonui o te hītori o Īhipa onamata. Ko te tihi o te hanganga piramita i puta i te wā o te Tuawhā o ngā Whare Ariki, me te piramita Nui o Giza, i hangaia mō Parao Khufu i te tau 2580–2560 BC.
2. Te Ine Taurite: Ngā Ariā me ngā Whakamahinga Taketake
Ko te ine whārite he peka o te pāngarau e ako ana i te whanaungatanga i waenga i ngā koki me ngā roa taha i roto i ngā tapatoru. Ko ngā ariā taketake o te ine whārite e pā ana ki ngā mahi sine (sin), cosine (cos), me te tangent (tan) o ngā koki o te tapatoru. E pā ana ēnei mahi e toru ki te roa o ngā taha o te tapatoru matau, ā, ka āwhina i te tatau i ngā koki me ngā taha kāore i te mōhiotia.
I roto i te horopaki o te hanganga o ngā piramiti, ka whakamahia te ine ine whārite hei whakatau i ngā pari o ngā taha me te tihi o te piramiti. E rua ngā ariā matua o te ine whārite e whakamahia pinepinetia ana ko te "pikinga," e inehia ana i roto i ngā nekehanga, i ngā hihi rānei, me te "pari," e pā ana ki te ōwehenga i waenga i te taha whakamuri me te waewae o te tapatoru i roto i te horopaki o te pari o te piramiti.
3. Te Whakamahinga o te Tauritenga i roto i te Hoahoa Piramiti
Ki te hoki anō ki te wā i mua i te hanganga o ngā tātaitai me ngā rorohiko, he mea whakamiharo pea te āhua o te ine ine ira tawhito. Heoi, i whakauruhia e ngā kaihoahoa o Īhipa o mua ngā ariā taketake o te ine ira ki roto i te hanganga o ngā piramita, pērā i te Piramita Nui.
a. Koki Piramiti
He tino tika te pikinga o te Piramiti Nui o Giza, tata ki te 51,5 nekehanga. Nā te aha i tutuki ai tēnei? Me tātari mā te whakamahi i te ine tapatoru. Mēnā ka whakaarohia he tapatoru matau i hangaia e te haurua o te turanga o te piramiti, te teitei o te piramiti, me te hypotenuse mai i te turanga ki te tihi, ka taea e tātou te whakamahi i te mahi tangent.
Ko te tātai o te koki piko (θ) ko te ōwehenga o te teitei o te pīramiti (h) ki te haurua o te roa o te turanga o te pīramiti (b/2).
Mena ko d te roa o te turanga o te piramiti, kāti:
tan(θ) = h / (d / 2)
Mā te koki o te piko i tatauhia he 51,5 nekehanga, ka whiwhi tātou:
parauri (51.5°) ≈ 1.273
Ko te tikanga o tēnei, ko te ōwehenga o te teitei o te piramiti ki te haurua o te roa o tōna turanga me tata ki te 1.273. Mā tēnei ka taea e tātou te whakatau tata i te teitei o te piramiti mēnā e mōhiotia ana te roa o tōna turanga.
b. Te whakamahi i te ariā Pythagorean
Haunga te mahi pātata, ka whakamahia hoki te ariā Pythagorean hei whakarite i te tika o ngā ōwehenga i roto i te hanganga piramiti. Mō te tapatoru matau i whakahuatia i mua ake nei, ka taea e tātou te whakamahi i te ariā Pythagorean:
a² + b² = c²
Ko a te teitei o te piramiti, ko b te haurua o te roa o te turanga, ā, ko c te teitei whakarara o te piramiti.
4. Ngā Taunakitanga o te Whakamahinga o te Tauritenga e ngā Kaihoahoa o Mua
Ahakoa he tokomaha e kī ana kāore pea ngā Ihipiana o mua i te mōhio ki ngā ariā ōkawa o te ine whārite, he nui tonu ō rātou mōhiotanga mahi hei whakamahi i ngā tikanga ōrite. Ko ngā taunakitanga o te tino tika e kī ana he tikanga matatau ā rātou mō te ine me te whakamahere.
E mōhiotia ana ko ngā kaihoahoa o taua wā i whakamahi i te pūnaha 'seked' o te ine i ngā koki mā te whakamahi i ngā ringa me ngā maihao. I roto i tēnei pūnaha, kotahi te 'ringa' he rite ki tētahi roa motuhake, ā, kotahi te 'maihao' he ordal iti ake – he tino rite ki te ariā hou o te trigonometry, e wehewehe ana i ngā koki kia wāhanga.
5. Te Whakataurite i te Pānga-toru i waenga i ngā Piramiti
Haunga te Piramiti Nui, kāore ngā piramiti Ihipiana katoa e whai i te koki pari kotahi. Hei tauira:
– He pari ake te koki piko o te Piramiti Whero i Dahshur, tata ki te 43 nekehanga, he rerekē ki te koki piko o te Piramiti Nui o Giza.
– Ko te Piramiti Piko, e mōhiotia ana mō tōna huringa o te koki piko mai i te 54 nekehanga ki te 43 nekehanga i waenganui.
E whakaatu ana ēnei rerekētanga i whakamātauhia hoki e ngā kaihoahoa o mua ngā koki me ngā tikanga rerekē, ā, i hangaia ai he piramita he ahurei ngā tau me ngā āhua.
6. Whakamutunga
Mā te whakakotahi i ngā mātauranga keri whenua me te pāngarau, ka kitea te matatau o ngā tikanga hoahoanga onamata mā te tātari i ngā piramita ine-ira. Kāore i te mea ko ngā koki me ngā ōwehenga anake i tatauhia e rātou me te auahatanga e ahua tawhito ana engari he tino whai hua. Nā te whakamahinga o te ine-ira i taea ai te hanga i ngā hanganga ehara i te mea he nui te tauine engari he pakari hoki te tika me te ōrite.
Mā te mārama ki te whakamahinga o te ine whārite ki ēnei piramita, ehara i te mea ka maioha noa tātou ki te pūkenga hangarau o Īhipa onamata engari ka ako anō hoki tātou mō te hītori o te whanaketanga o te pāngarau i roto i te hoahoanga onamata. Ko ngā piramita he taunakitanga nui o te whakakotahitanga o te toi me te pūtaiao i eke ki ngā taumata tino teitei mano tau i mua i te hanganga o tō tātou hangarau hou.
