Umlando theorem kaPythagoras. ubufakazi

Umlando theorem kaPythagoras has zeminyaka eziningana. Isimangalo esishoyo ukuthi esigcawini hypotenuse ilingana isamba sezikwele imilenze, kwakwaziwa eside ngaphambi kokuzalwa sezibalo ngesiGreki. Nokho, theorem kaPythagoras, umlando ekudalweni nobufakazi lesibopho yayo ngoba iningi kangakanani ngala ososayensi. Ngokusho kweminye imithombo, isizathu salokhu kwaba ubufakazi lokuqala theorem, okwakubekelwa inikwa amandla yi-Pythagoras. Nokho, abanye abacwaningi abathi ngokwezinga ekuphikiseni leli qiniso.

Umculo kanye logic

Ngaphambi esikutsho kuwe indaba savela kanjani theorem kaPythagoras, kafushane Biography of sezibalo. Wayehlala BC VI leminyaka. Usuku lokuzalwa Pythagoras 570 BC. e, endaweni -. esiqhingini Samos. On ukuphila usosayensi sika kancane yaziwa. Imininingwane omlando womuntu e imithombo ngesiGreki iphothene nge eqanjiwe sobala. On emakhasini azibhala kubonakala ayisi- omkhulu, umyalo omkhulu yamagama kanye nekhono ukukholisa. By endleleni, lokhu kungani sezibalo ngesiGreki Pythagoras futhi ngokuthi, okungukuthi "inkulumo ngezinkulumo ezithonyayo". Ngokusho kwenye inguqulo, ukuzalwa ayisi- esizayo wabikezela Oracle. Ubaba behlonipha wakhe Bamnqamba ngu Pythagoras.

Sage wafundelwa izingqondo olukhulu isikhathi. Phakathi abafundisi Pythagoras abasha Pherecydes avele Germodamant Sirossky. Eyokuqala bagxilisa kuye uthando lomculo, ifilosofi yesibili wafundisa. Zombili lezi sciences izohlala yilokho esigxila kukho lapho usosayensi othile kukho konke ukuphila kwakhe.

Imfundo kule oneminyaka engu-30 isikhathi eside

Ngokusho kwenye inguqulo, ngokuba yonke into eziyibonayo izinsizwa, Pythagoras kwesokunxele ezweni lakubo. Waya ufune ulwazi eGibhithe, wahlala khona, ngokusho emithonjeni ehlukahlukene, kusukela eminyakeni engu-11 kuya ku-22, bese sathathwa isiboshwa wathumela eBhabhiloni. Pythagoras wakwazi ukuzuza emalungiselelweni ayo. Iminyaka 12, wafunda isayensi yezibalo, i-geometry, futhi magic esimweni lasendulo. Samos Pythagoras awabuyelanga kwaze kwaba seminyakeni engu-56 ubudala. Lapha, kuyilapho imithetho Polycrates engumashiqela. Pythagoras ayikwazanga ukwamukela isimiso sezombangazwe enjalo, futhi ngokushesha waya eningizimu ye-Italy, lapho ibekwe koloni yesiGreki Croton.

Namuhla ungakwazi ngokuqiniseka ukuthi Pythagoras wayeseGibhithe neBabiloni. Mhlawumbe washiya Samos, kwathi kamuva kwaba khona manjalo Croton.

Pythagoreans

Umlando theorem kaPythagoras ezithuthukisa adalwe isazi sefilosofi esingumGreki lesikole. Lobu buzalwane zenkolo-nezimiso zokuziphatha washumayela ukunamathela zokuphila ethile, wafunda izibalo, i-geometry nesayensi yokuhlolwa kwezinkanyezi, eyingoduso ekuhloleni ohlangothini zefilosofi ezingaqondakali of izinombolo.

Zonke abafundi kokuvula sezibalo ngesiGreki isibaluli kuye. Nokho, umlando umsuka theorem kaPythagoras uboshelwe wokuphila lasendulo kuphela sefilosofi. Kusolwa ukuthi wayenike amaGreki lwati lolutfolakele iBhabhiloni neGibhithe. Kukhona inguqulo wathola ngempela theorem phezu ratios imilenze kanye hypotenuse, engazi mayelana impumelelo bezinye izizwe.

Theorem Pythagorean: umlando ukutholakala

Kwezinye imithombo ngesiGreki ukuchaza injabulo Pythagoras, lapho ekwazi ukufakazela theorem. Ukuze kuhlonishwe lo mcimbi, wayaleza umhlatshelo konkulunkulu efomini zamakhulu yezinkunzi, wenza idili. Nokho, ezinye izazi ikhomba ukungabi nakwenzeka kwento lesi senzo ngenxa ubunjalo Pythagoreans ukubukwa.

Kukholakala ukuthi indatshana "Imisuka", adalwe Euclid, umlobi kunikeza ubufakazi theorem, umlobi zazo isazi sezibalo esikhulu ngesiGreki. Nokho, lo mbono ucingo awasekelwe yiwo wonke. Ngakho, ngisho sefilosofi lasendulo Neoplatonist Proclus waveza ukuthi umbhali wencwadi ngenhla "Principia" ngokwaso ubufakazi Euclid.

Kungakhathaliseki ukuthi laliyini, kodwa owokuqala lokwakha theorem ukuthi namanje kwakungelona Pythagoras.

Ancient Egypt neBhabhiloni

ifayela echaza ifomu Pythagorean, elibhekene nomse- indaba yendalo esihlokweni, ngokuvumelana sezibalo German Cantor, okwakwaziwa ngokuthi ekuqaleni njengoba 2300 BC. e. eGibhithe. Izakhamuzi wokubusa eSigodini saseNayile uFaro Amenemhat lasendulo ngangazi nokulingana Februwari ³ + 4 = 5 ^{² ².} Kusolwa ukuthi ngosizo calantsatfu izinhlangothi 3, 4 no-5 salo mGibhithe "intambo natyagivateli" ujenga engeli.

ifayela echaza ifomu eyaziwayo Pythagoras eBhabhiloni. Ezibhebheni zobumba yangekhulu 2000 BC futhi isibaluli wokubusa King uHammurabi, wathola i ukubala esikiselwayo hypotenuse unxantathu kwesokudla.

India neChina

Umlando theorem kaPythagoras ehlangene impucuko of India neChina lasendulo. Indatshana "Xuan Zhou bi jin" siqukethe iziyalo unxantathu waseGibhithe (ezinhlangothini zalo ezihlobene njengoba 3: 4: 5) beyaziwa e China kudala njengoba e XII. BC. e. nasezingxenyeni VI. BC. e. wezibalo lokhu isimo ukwazi ifomu jikelele theorem.

Ukwakhiwa ilungelo engela unxantathu usebenzisa waseGibhithe achazwa indatshana Indian "Sulva Sutra" yangekhulu VII-V cc. BC. e.

Ngakho, umlando theorem kaPythagoras ukuba nesikhathi lokuzalwa sezibalo ngesiGreki sefilosofi iphindela amakhulu amaningana eminyaka.

ubufakazi

Engakabi yayo theorem wayengomunye walaba geometry ecashile. Umlando ubufakazi theorem ka Pythagoras, cishe waqala ngokucabangela i equilateral unxantathu wesokudla. On hypotenuse yayo futhi izinhlangothi zakhiwa izikwele. Lowo 'wakhula "phezu hypotenuse, izokuba onxantathu omane asezinyaweni ilingane kuqala. Ngakho-ke, izikwele phezu cathetus aqukethe onxantathu amabili anjalo. ukumelwa Simple ingcaca libonisa ngokucacile ukuba yiqiniso kwalesi ukugomela washayelwa ngesimo theorem abadumile.

Enye ubufakazi elula ehlanganisa geometry ne-Aljibhra. Four onxantathu kwesokudla angled ezifanayo ne izinhlangothi a, b, c basondela ukuze tikwele ezimbili: ohlangothini elingaphandle nge (c +) futhi ohlangothini owangaphakathi nge. Ngakho indawo encane isikwele ilingana ^2. Indawo ebalisisiwe ezinkulu kusukela isamba izindawo isikwele ezincane nazo zonke onxantathu (endaweni unxande unxantathu, sikhumbula, ibalwa ngu ifomula (A * B) / 2), okusho ² + 4 * ((A * B) / 2), okuyinto ilingana ² + 2av. Le ndawo kwesikwele ezinkulu ingabalwa ngendlela ehlukile - njengoba umkhiqizo izinhlangothi ezimbili, okungukuthi, (a + b) ^2, okuyinto okulingana ² + ² + 2av. It kuvela:

futhi 2av + ² + ² + ² = 2av,

futhi ² + ² = s ^2.

Kunezinhlobo eziningi ubufakazi lokhu ifayela echaza ifomu. Ngaphezu kwazo wasebenza futhi Euclid, futhi ososayensi Indian, futhi uLeonardo da Vinci. Ngokuvamile zo lasendulo yaholela imidwebo, izibonelo zazo zitholakala ngenhla futhi musa bathole ncazelo, ngaphandle amanothi, "Bheka!" Ukuba lula kwezincazelo bonakaliso weJiyomethri enikeziwe kukhona abanye imibono nolwazi futhi akazange zidinga.

Umlando theorem kaPythagoras, ngokufingqiwe isihloko okuxosha inganekwane mayelana ngomsuka wayo. Nokho, kunzima ukucabanga ukuthi igama sezibalo esikhulu ngesiGreki sefilosofi wake phezani nalo.