I ka moolelo o ka Pythagorean theorem. ke hooiaio

I ka moolelo o ka Pythagorean theorem loaʻa paha kekahi mau millennia. Ke koi ana e olelo ana i ke kahua o ka hypotenuse, ua like me ka huina o na mika pāhoʻonui lua o nā wāwae, ka mea iʻikeʻia loa ma mua o ka hānauʻana o ka Helene mathematician. Naʻe, i ka Pythagorean theorem, ka mōʻaukala o ka hanaia'na, a me ka hoike ana o kona nakinakiia no ka hapanui o ia mea i kēia mau kānakaʻepekema. E like me ia i kekahi mau kumu, i ke kumu no keia i ka mea mua hooiaio o ka theorem, i ka mana e Pythagoras. Naʻe, kekahi noiʻi hōʻoleʻia kāna i kēia mea.

Music a me ke kūpili

Mua mākou iāʻoe i ka moʻolelo Hawaiʻi Pythagorean theorem, pokole Kawaihae o mathematician. He noho ma ka VI kenekulia BC. Ka lā o ka hanau ana o Pythagoras 570 BC. E, he wahi -, i ka mokupuni o Samo. Ma kekahi nä känaka 'epekema ka ola ka mea, ua ike i ka uuku. Biographical 'ike i loko o Greek kumu i ulana pūʻia me ka maopopo fiction. Ma ka 'aoʻao o ka hoonoho eia kahi mea akaka he kumu nui, nui kauoha o ka hua'ōlelo, a me ka hiki, e hoohuli. Ma ke ala, keia mea ke kumu no ka Helene mathematician Pythagoras, a kapa aku la, i ka mea "imua oiala, olelo". E like me ka hiki i kekahi mana, i ka hanau ana o kekahi wā e hiki mai kumu wānana kahi e'ōlelo ai. Makua i loko o kona hanohano i kapaʻia ke keiki ma ka Pythagoras.

Kumu aʻo me ka manaʻo nui o ka manawa. I waena o nā kumu o ka opiopio Pythagoras a me Pherecydesʻikeʻia Germodamant Sirossky. Ka mua luna o ia ia i aloha no mele, i ka lua o ka ao mai akeakamai. Ua o kēia mau sciences e noho i ka pulakaumaka o ke nä känaka 'epekema ma kona ola.

Hoʻonaʻauao ma o ka 30-makahiki-lōʻihi

E like me ka hiki i kekahi mana, i nā kānaka uʻi inquisitive, Pythagoras haʻalele i kona'āina hānau. He hele aku e nana i ka ike i loko o Aigupita, kahi āna i noho ai, e like me na kumu, mai ka 11 a hiki i 22 makahiki, a laila, i lawe pio, a hoouna aku ai i Babulona. Pythagoras ua hiki e mai kona ai pōmaikaʻi ai. No ka 12 makahiki, oia aʻo makemakika, anahonua, a me ka hana kilokilo i loko o ka moku'āina kahiko. Samo Pythagoras,ʻaʻole hoʻi i hiki i 56 makahiki. Eia, oiai na rula o ka Wiliama Polycrates. Pythagoras hiki ole ia ia ke ano pili aupuni, a koke hele aku la a hiki i kaʻaoʻao hema o Italy, kahi āna i waiho Greek lēpela o Croton.

I kēia lā hiki ole oe e olelo aku ai no ka oiaio ina Pythagoras i loko oʻAigupita, a Babulona. Paha ia i haʻalele Samo, a ma hope, hele koke ma Croton.

Pythagoreans

I ka moolelo o ka Pythagorean theorem pili ana i ke kūpono 'ana hanaia ma ka Helene poe akeakamai o ka kula. Kēia haipule-pono launa hoahānau i hai adherence i kekahi lifestyles, a nānā aku makemakika, anahonua, a kilohōkū, i komo i loko o ke ao o kaʻaoʻao philosophical a me mystical o ka helu.

A pau i nä haumäna wehe i ka Helene mathematician wahi iā ia. Naʻe, i ka mōʻaukala o ke kumu o ka Pythagorean theorem ua paa ia e kahiko biographers wale e kekahi poe akeakamai. Ua Ua ea ae ka hana i ka mea i haawi mai i ka poe Helene i ka ike i loaa i loko o Babulona a me Aigupita. Aia mea no hoi ka mana e hiki ia ia maoli ike i ka theorem ma ka lākiō. O na wawae, a me ka hypotenuse, i ka ike e pili ana i ka piʻi like o nā lāhui kanaka.

Pythagorean Theorem: mōʻaukala o ka loaʻa

Ma kekahi Greek kumu wehewehe i ka olioli o Pythagoras, ia ia i hiki ke hooiaio i ka theorem. Ma ka hanohano o keia hanana, ua kauoha i ka mohai ana i na akua ma ke ano o ka haneri o nā bipi kāne, a hana ihola i kaʻahaʻaina. Kekahi mau haumana, nae, kuhi i ka impossibility o ia i hana ma muli o ia i ke 'ano o ka Pythagoreans manao.

Ua Ua manaoio aku ia i loko o ka hoonoho "hehee wale", i hanaʻia e Euclid, ka mea kākau haawi hooiaio o ka theorem, i ke kumu o ka a ua ka nui Helene mathematician. Naʻe, ua manao uaʻaʻole i kākoʻo 'ia e nā mea a pau. No laila,ʻo ka mea kahiko poe akeakamai Neoplatonist Proclus kuhikuhi mai i ka mea kākau o ka luna i loko o ka "He" mea wale maopopo o Euclid.

Ka mea a ka mea, ua, akā, me ka mea mua, e formulate i theorem i no ua ole Pythagoras.

Makamua Aigupita a me Babulona

Pythagorean theorem, i epa a me ka moʻolelo o ka hanaia'na i loko o ka pauku, e like me ka German mathematician Cantor, i ikeia ma ke kakahiaka nui me 2300 BC. e ka. i loko oʻAigupita. Na kamaaina kahiko o ka noho alii ana o ka muliwai Valley Parao Amenemhat au i ike i ka pololei February ³ + 4 = 5 ^{² ².} Ua Ua ea ae ia me ke kōkua o ke triangle me ka aoao 3, 4 a me 5 o ka Aigupita "kaula natyagivateli" hoalaala pana pua.

Ike theorem o Pythagoras ma Babulona. Ma ka lepo o na papa io ka launa pū mai ka 2000 BC a wahi i ka noho alii ana o King Hammurabi, 'ike akula i ka He kokekau wale i ka ho omaulia ana o ka hypotenuse o ka triangle akau.

India a China

I ka moolelo o ka Pythagorean theorem ua pili me ka maikai ana kahiko o Inia a me Kina. Hoonoho aku "Xuan Zhouʻelua-jin" ÷ kuhi i Aigupita triangle (kona aoao hai aku me 3: 4: 5) Ua, ua hoikeia mai ma Kina i kakahiaka me ka XII. BC. E, a me ka VI. BC. e ka. makemakika o kēia moku'āina i ka nui kino o ka theorem.

Ua ho'ākāka? ieoaeunoai o ka pono huina triangle hoʻohana 'ana iʻAigupita i loko o Mauna hoonoho "Sulva Sutra" ka launa pū mai VII-V CC. BC. e ka.

Penei, ka mōʻaukala o ka Pythagorean theorem a hiki i ka manawa o ka hanau ana o ka Helene mathematician a me ka poe akeakamai hele hoʻi kekahi mau haneri makahiki.

hoike

I loko o kona ola ana theorem i kekahi o ka nń ku anahonua. Mōʻaukala o ka hooiaio ana o ka theorem o Pythagoras, paha, hoomaka ae la me ka noonoo ana o ka equilateral akau triangle. Ma kona hypotenuse a me ka aoao i kūkulu mika pāhoʻonui lua. Ka kekahi mea "e ulu mai" ma o ka hypotenuse, e iloko o ka eha triangle mauna mea e like me ka mua. Nā mika pāhoʻonui lua ma luna o ka cathetus pela i komo o na puu triangle mauna. Simple Kimia e hoohalike ai maopopo hōʻike i ka ho'ōia o ka assertion ua kālaiʻia i loko o ka palapala o ka theorem kaulana.

Kekahi poe noonoo ole maopopo hiehie anahonua me ka hōʻailona helu. Lau'ālike akau-huina triangle mauna me ka aoao i kekahi, e, pela aku e holo ai e like me ka hana mau mika pāhoʻonui lua: mawahoʻaoʻao me (ka + c) a me kaʻaoʻao ma loko a me. Pela he uuku wahi o ka hale, ua like ia ^2. Ka wahi o ka nui o ia mau hōʻailona, mai ka huina o na mau mea o ka uuku huinahalike a me nā mea a pau triangle mauna (huinahń wahi o ka triangle, ua keia iloko o, he pōpilikia ma ka haʻilula (A * B) / 2), oa ² + 4 * ((A * B) / 2), a mea like i ² + 2av. Ka wahi o ka hale nui hiki ke mau hōʻailona i loko o kaʻokoʻa ala - like me ka huina hoonui o kaʻaoʻaoʻelua, i mea, (he + b) ^2, i mea like me ka ² + ² + 2av. Ua huli mai:

a me ka 2av + ² + ² + ² = 2av,

a ² + ² = mau ^2.

Ua nui Lolina o ka hooiaio ana o keia theorem. Ma luna o ia mau mea paakiki a me ka Euclid, a me Indianʻepekema, a me Leonardo ka Vinci. Pinepine kahiko sages alakai Nails, examples o i i aia ma luna a me ka mai ole i kekahi wehewehe, 'ē aʻe ma mua o memo, "E nana!" Ka pono io o geometric hoike nae he mea kekahi ike manaʻo, a i ole he pono.

dispels i ka moolelo o ka Pythagorean theorem, ua hoʻoʻuluʻulu manaʻo i loko o ka 'atikala i ka nā kaʻao e pili ana i kona kêia kanaka. Naʻe, ka mea, ua paakiki ka manao wale ana i ka inoa o ka nui Helene mathematician a me ka poe akeakamai loa hooki me ka mea e e pili.