Pythagoras me te Rapunga Whakaaro o ngā Tau
He tohunga whakaaro me te tohunga pāngarau rongonui a Pythagoras i Kariki onamata, e kiia ana ko ia te matua o te rapunga whakaaro o ngā tau. I whānau ia i te tau 570 BC i te moutere o Samos i Ionia, i Kariki, ā, i mate i te tau 495 BC. E mōhiotia ana a Pythagoras mō ngā āhuatanga maha o ana whakaaro me ana mahi, engari ko tētahi o ngā mea tino rongonui ko ana takoha ki te pāngarau, me te ariā tau anō hoki. Ka tirohia hohonutia e tēnei tuhinga a Pythagoras me te rapunga whakaaro o ngā tau, te take me te pēhea i whai wāhi nui ai ngā tau ki te tirohanga ao a Pythagoras, me tana taonga tuku iho whakaaro me te pāngarau, e mau tonu ana te hiranga i ēnei rā.
Te Oranga me te Papamuri o Pythagoras
I whānau mai a Pythagoras i Samos, engari i haereere nui ia ki ngā wāhi pērā i a Īhipa me Pāpurona. I a ia e haereere ana, i ako ia i ngā momo kaupapa ako, tae atu ki te pāngarau, te whetū, me te rapunga whakaaro. I te mutunga, ka noho a Pythagoras ki Croton (kei te tonga o Itari ināianei), i reira ka whakatūria e ia tētahi hapori whakapono me te rapunga whakaaro e mōhiotia ana ko te Pythagoras Sect.
Ehara tēnei hapori i te kura noa iho, engari he rōpū whānau anō hoki me tētahi hanganga me ngā ture motuhake. E piri ana ngā mema ki ngā aratohu kai me te momo noho pakari, ā, e whakapono nui ana ki te oranga tonutanga o te wairua me te whānautanga anō. E whakapau kaha ana hoki rātou ki te tūhura i ngā whanaungatanga ngaro me te pāngarau o roto i te ao tūroa.
Te Rapunga Whakaaro a Pythagorean me te Ariā o ngā Tau
Ko tētahi o ngā takoha nui a Pythagoras ko te ariā ko te tau te pūtake o ngā mea katoa, ā, ko te ao whānui e whakahaeretia ana e ngā mātāpono pāngarau. I whakapono a Pythagoras me āna akonga ka taea te whakamārama i ngā mea katoa mā roto i ngā tau me ngā whanaungatanga tau. Ko tēnei tirohanga te pūtake o te mea e kiia nei ko te "whakaaro mō ngā tau" a Pythagoras.
Ngā Mātāpono Matua o te Rapunga Whakaaro o ngā Tau
1. Ngā Tau hei Uho o Ngā Mea Katoa:
I whakaako ngā Pythagoras ko ngā tau te mauri taketake o te ao whānui. Hei tauira, i kitea e rātou ka taea te whakamārama i ngā whanaungatanga puoro mā roto i ngā ōwehenga o ngā tau katoa. I roto i tana rangahau mō ngā aho wiri, i kitea e Pythagoras ka puta ngā wā whakaōrite i roto i ngā ōwehenga māmā—pērā i te 1:2 (octave), 2:3 (quint), me te 3:4 (quart). I whakaatuhia e tēnei ehara i te mea he taputapu pāngarau noa ngā tau, engari ko te pūtake hoki o te whakaōrite me te ataahua o te taiao.
2. Te Mutunga Kore me te Whakawhirinakitanga Tau:
I tūhuratia hoki e Pythagoras te ariā o te mutunga kore e pā ana ki ngā tau. Ko ngā tau taurite (ka taea te whakaatu hei hautanga o ngā tau katoa e rua) he maha ngā tau e whai āhua ōrite ana, i roto i te ariā Pythagoras. Heoi, i kitea anō e rātou he tau kāore e taea te whakaatu mā te ōwehenga, e mōhiotia ana ko ngā tau taurite. Nā tēnei kitenga i whakararu i tō rātou whakapono ki te raupapa tau me te raupapa ao whānui, e whakaatu ana i te uauatanga hohonu o te ao.
Te ariā Pythagorean
Ko te Pythagoras Theorem, tētahi o ngā takoha pāngarau rongonui a Pythagoras, e kī ana i roto i te tapatoru matau, ko te tapawhā o te roa o te hypotenuse he ōrite ki te tapeke o ngā tapawhā o te roa o ngā waewae e rua. Ka taea tēnei te whakatakoto penei:
a² + b² = c²,
ko 'c' te roa o te hypotenuse, ā, ko 'a' me 'b' ngā roa o ngā waewae e rua e hanga ana i tētahi koki hāngai.
Ehara i te mea he hua pāngarau nui tēnei ariā engari he whakaaturanga anō hoki o te whakapono a Pythagorean ko ngā tau me ngā whanaungatanga tau te mauri taketake o te ao whānui. I roto i te tauira Pythagorean, ka honoa e tēnei ariā te āhuahanga me te pāngarau, e whakaatu ana i te whakarite a ngā tau i te hanganga o te wāhi ā-tinana.
Te whakapono Pythagorean: Te hapori me te whakapono ngaro
Ehara i te mea he huinga ariā pāngarau me te rapunga whakaaro noa iho te whakapono Pythagorean, engari he kaupapa wairua me te hapori whakapono anō hoki. I whai ngā mema o te hapori Pythagorean i ngā ture tino motuhake, tae atu ki te kai huawhenua me ngā ture mō te parakore, tae atu ki ā rātou ake whakatau matatika.
Te Matakite a Pythagorean
I mōhiotia anō a Pythagoras hei tohunga matakite. I whakapono ana akonga he mea ora tonu te wairua e whakawhānau houtia ana, ā, mā te oranga tapu me te noho auau ka taea te horoi i te wairua i te kino me te whakaara ake i a ia ki tētahi taumata teitei ake o te oranga. I whakaarohia he mea nui ngā tau me ō rātou whanaungatanga ki te ao whānui me te wairua.
I whakaako anō a Pythagoras he "nomos" tō ngā mea katoa, arā, he ture taiao , ka taea te mārama mā te ako i ngā tau me ngā ōwehenga. Hei tauira, i roto i ngā mahi toi me ngā waiata, i whakamahia e ngā Pythagoras ngā mātāpono pāngarau hei rapu i te rangimarie me te tikanga.
Te Taonga Tuku Iho a Pythagoras i roto i te Pāngarau me te Rapunga Whakaaro
He whānui te taonga tuku iho a Pythagoras, e kapi ana i ngā mara maha i tua atu i te pāngarau. Nā tana rapunga whakaaro mō te tau hei kaupapa matua o ngā mea katoa i awe ngā whakaaro matatika me te pūtaiao o muri mai.
Te Awe i roto i te Pāngarau
He maha ngā hua me ngā ariā i kitea tuatahitia, i akohia rānei e Pythagoras me āna akonga, kua waiho hei pūtake mō te ako tonu i te pāngarau. Ko te ariā Pythagoras tētahi o ngā ariā matua tino nui o te pāngarau, ā, kei te whakaakona tonutia puta noa i te ao.
Te Awe i roto i te Rapunga Whakaaro
I awe a Pythagoras i te tini o ngā tohunga whakaaro nui, tae atu ki a Plato rāua ko Aristotle. I tino miharo a Plato ki ngā ariā a Pythagoras mō te tau me te whakakotahitanga o te ao, ā, i whakaurua e ia ki roto i tana ake rapunga whakaaro. Ko te ariā a Plato mō te "ao o ngā whakaaro," e taea ai te mārama ki te ao tūturu mā te mātauranga parakore anake, ehara i te tirohanga ā-pāngarau, i ahu mai i te tirohanga a Pythagoras mō te tau me te pāngarau hei kī ki te mārama ki te ao whānui.
Puoro me te Harmoni
He mea nui anō hoki ngā takoha a Pythagoras ki te ariā puoro. He maha ngā mātāpono taketake o te ariā puoro o te Hauāuru e ahu mai ana i ngā kitenga a Pythagoras mō ngā whanaungatanga tau me te rangimārie. Ko te tirohanga ka taea te whakarite puoro kia rite ki ngā mātāpono pāngarau kei roto tonu i te ariā puoro tae noa ki tēnei rā.
Whakamutunga
Kāore e taea te wehe i a Pythagoras me te rapunga whakaaro o te tau mai i te hītori o te pāngarau me te rapunga whakaaro o te Hauāuru. Nā āna whakaakoranga mō te mauri o te tau me te whakakotahitanga o te ao whānui, i waiho e Pythagoras tētahi taonga tuku iho e hipa ana i ngā kaupapa ako me te wā. Mai i ngā ariā matawhenua taketake ki ngā ariā ngaro o te ao whānui, kei te whai tikanga tonu ngā mātāpono a Pythagoras i roto i ngā mara ako me ngā mahi maha.
Ina ako tātou i te pāngarau, ina whakaaroaro rānei ki te ataahua o te ao tūroa, ka hoki anō tātou ki ngā mātāpono taketake i titoa tuatahitia e Pythagoras me tōna hapori. I tēnei tikanga, ko Pythagoras me te rapunga whakaaro o te tau he piriti nui i waenganui i te pāngarau me te rapunga whakaaro, e whakamahara ana i a tātou ko te ao, me tōna āhua pai me tōna ataahua katoa, he mea ngaro e tatari ana kia whakamāramahia e ngā tau me ngā ōwehenga e huna ana i raro i tōna mata.
