Euclid

Euclid a i ʻole Euclid (c. ʻO ka makemakika mua o ke kula ʻo Alexandria.

I kāna hana nui "Nā Hoʻomaka" ua wehewehe ʻo ia i ka planimetry, stereometry a me nā kumumanaʻo helu. ʻO ka mea kākau o nā hana ma optics, mele a me astronomy.

Nui a hewahewa nā mea i hoihoi ʻia i loko o ka moʻolelo pilikino o Euclid, a mākou e hoʻopā aku ai i kēia ʻatikala.

No laila, eia kahi moʻolelo pōkole o Euclid.

Kawaihae o Euclid

Ua hānau ʻo Euclid ma kahi o 325 BC. e., eia naʻe, kuhi kēia lā. ʻAʻole maopopo kona wahi hānau.

Hōʻike kekahi mau mea kākau moʻolelo o Euclid ua hānau ʻia ʻo ia ma Alexandria, ʻo kekahi poʻe - ma Turo.

ʻO ke kamaliʻi a me ka ʻōpio

ʻO ka ʻoiaʻiʻo, ʻaʻohe mea i ʻike ʻia e pili ana i nā makahiki mua o ko Euclid ola. Wahi a nā pepa ola, ua hoʻohana ʻo ia i ka hapa nui o kona ola makua ma Damaseko.

ʻAe ʻae ʻia no Euclid kahi ʻohana waiwai. ʻO kēia ma muli o ke aʻo ʻana ma ke kula Athenian o Plato, kahi mamao loa mai ka poʻe ʻilihuna e hiki ai ke aʻo.

He mea pono e hoʻomaopopo he mākaukau ʻo Euclid me nā manaʻo akeakamai o Plato, ma nā ʻano he nui e kaʻana like ana i nā aʻo a ka mea manaʻo kaulana.

ʻO ke kumu, ʻike mākou e pili ana i ka moʻomeheu o Euclid mahalo i nā hana a Proclus, ʻoiai ʻo ia ke ʻano o kona ola ʻana ma kahi o 8 mau kenekulia ma hope o ka makemakika. Eia kekahi, ua loaʻa kekahi mau ʻike mai ke ola o Euclid i nā hana a Pappa o Alexandria a me John Stobey.

Inā hilinaʻi ʻoe i ka ʻike o nā ʻepekema hou loa, a laila he kanaka lokomaikaʻi, a me ka noʻonoʻo pono ʻo Euclid.

Ma muli o ka liʻiliʻi o ka ʻikepili e pili ana i kahi kāne, manaʻo kekahi mau loea e hoʻomaopopo ʻia ʻo Euclid ma ke ʻano he hui o nā ʻepekema ʻo Alexandria.

Makemakika

I kona mau manawa manawaleʻa, makemake ʻo Euclid e heluhelu i nā puke i loko o ka Hale Waihona Puke ʻo Alexandria. Ua aʻo ʻo ia i ka makemakika hohonu a ʻimi pū kekahi i nā loina geometric a me ke kumumanaʻo o nā helu kūpono ʻole.

E hoʻolaha koke ʻo Euclid i kāna mau ʻike ponoʻī a me kāna mau ʻike i kāna hana nui "Inception". Ua kōkua nui kēia puke i ka hoʻomohala ʻana i ka makemakika.

Loaʻa iā ia he 15 puke, ʻo kēlā me kēia mea i kau i ka ʻepekema kikoʻī.

Ua kūkākūkā ka mea kākau i nā waiwai o nā parallelograms a me nā triangles, i manaʻo ʻia i ka geometry o nā pōʻai a me ka manaʻo maʻamau o nā kaulike.

Eia nō naʻe ma "Elemene" ua nānā ʻia ka manaʻo o nā helu. Ua hōʻoia ʻo ia i ka palena ʻole o ka papa o nā kuhina nui, ua ʻimi a hiki i nā helu kūpono a huki i kahi manaʻo e like me GCD - ka mea hoʻokaʻawale maʻamau nui loa. I kēia lā, ua kapa ʻia kēia mahele e kapa ʻia ʻo Euclid's algorithm.

Eia hou, i loko o ka puke ua kahakaha ka mea kākau i nā kumu o ka stereometry, hōʻike i nā manaʻo e pili ana i nā puke cones a me nā pyramid, me ka poina ʻole e haʻi i nā lakio o nā wahi o nā pōʻai.

Aia i loko o kēia hana ka ʻike nui, nā hōʻike a me nā ʻike i manaʻo ʻia he nui nā mea kākau moʻolelo o Euclid e manaʻo ʻia ua kākau ʻia nā "Kumumanaʻo" e kahi hui o ka poʻe.

ʻAʻole kāpae ka poʻe loea i ka hiki i nā ʻepekema e like me Archytas o Tarentum, Eudoxus o Cnidus, Theetetus o Athens, Gipsicle, Isidore o Miletus a me nā poʻe ʻē aʻe i hana ma ka puke.

No nā makahiki he 2000 e hiki mai ana, ua lilo nā hoʻomaka me he puke aʻo kumu ma ke geometry.

Pono e hoʻomaopopo ʻia ʻaʻole ka hapanui o nā mea i loaʻa i loko o ka puke i kā lākou ʻike ponoʻī, akā ʻo nā manaʻo i ʻike ʻia ma mua. ʻO ka ʻoiaʻiʻo, ua hana maʻalahi ʻo Euclid i ka ʻike i ʻike ʻia i kēlā manawa.

Kaawale mai nā Kumumanaʻo, ua paʻi ʻo Euclid i kekahi mau hana ʻē aʻe e pili ana i nā optics, ke ala hele o ka ʻoni ʻana o nā kino, a me nā kānāwai o ka mīkini. ʻO ia ka mea kākau o nā helu helu kaulana e hoʻomaʻamaʻa ʻia nei i ka geometry - ka mea i kapa ʻia ʻo "Euclidean kūkulu".

Ua hoʻolālā pū ka ʻepekema i kahi mea kani no ke ana ʻana i ka pitch o ke aho a aʻo i nā kaulike wāwaena, i alakaʻi ʻia ai ka hoʻokumu ʻana i nā mea kani kīpona.

Akeakamai

Ua hoʻomohala ʻo Euclid i ka manaʻo akeakamai o Plato o 4 mau mea, i pili me 4 polyhedra maʻamau:

ʻo ke ahi kahi tetrahedron;
he ʻekelikone ka ea;
honua he pahu;
he icosahedron ka wai.

I kēia pōʻaiapili, "Hoʻomaka" hiki ke hoʻomaopopo e like me ke aʻo kumu i ke kūkulu ʻia ʻana o "nā pā paʻa Platonic", ʻo ia hoʻi, 5 polyhedra maʻamau.

ʻO ka hōʻoia o ka hiki ke kūkulu i kēlā mau kino ke hoʻopau me ka ʻōlelo ʻaʻohe mea kino maʻamau ʻē aʻe ma kahi o nā mea i hōʻike ʻia 5.

He mea pono e hoʻomaopopo ʻia e pili ana nā theorems a me nā postulate o Euclid e kahi pilina pili e kōkua ai e ʻike i ke kaulahao kūpono o nā manaʻo o ka mea kākau.

Ke ola pilikino

ʻAʻole maopopo iā mākou i kekahi mea e pili ana i ko Euclid ola pilikino. Wahi a kekahi kaao, ua huli ʻo King Ptolemy, ka mea makemake e aʻo i ka geometry, i kahi makemakika no ke kōkua.

Ua noi ka mōʻī iā Euclid e hōʻike iā ia i ke ala maʻalahi loa i ka ʻike, i pane ʻia e ka mea noʻonoʻo: "ʻAʻohe ala aliʻi i ka geometry." ʻO ka hopena, ua lilo kēia ʻōlelo i mea eheu.

Aia kekahi hōʻike e wehe ʻo Euclid i kahi kula makemakika pilikino ma ka Waihona Puke o Alexandria.

ʻAʻole i kū hoʻokahi kiʻi pono o ka ʻepekema i kēia lā. No kēia kumu, ʻo nā kiʻi pena a pau a Euclid a me nā kiʻi kālai ʻia he kiʻi wale nō ia o nā manaʻo o kā lākou mea kākau.