Imbali theorem kaPythagoras. le ubungqina

Imbali theorem kaPythagoras iye zeminyaka emininzi. Ibango esichaza ukuba isikweri hypotenuse lilingana udibaniso lwezikweri imilenze, Kwazeka oko elide phambi kokuzalwa sezibalo zamaGrike. Nangona kunjalo, lo theorem kaPythagoras, imbali kwendalo kunye ubungqina ebotshiwe yayo uninzi lwalo ngala izazinzulu. Ngokutsho kweminye imithombo, isizathu sokuba le ubungqina wokuqala theorem, leyo enikwe kaPythagoras. Noko ke, abanye abaphandi aphikise le nto.

Umculo kunye nengqondo

Ngaphambi kokuba ndithi kuni ibali wavela njani theorem kaPythagoras, ngokufutshane biography of yezibalo. Wayehlala BC ngenkulungwane VI. Umhla wokuzalwa bakaPythagoras 570 BC. e, indawo -. kwisiqithi Samos. On ubomi sisazinzulu xa yaziwa kancinane. ulwazi oluchaza ngazo kwimithombo zamaGrike zimanyene kunye fiction ezicacileyo. Kumaphepha azibhala kubonakala kwesilumko elikhulu, myalelo mkhulu kwamagama kunye nokukwazi ukuba beyiseke. Hi ndlela leyi, le nto sezibalo Greek Pythagoras kunye yiAkeldama, oko kukuthi "ngentetho egudileyo". Ngokutsho kwenye inguqulelo, ukuzalwa kwesilumko kwangaphambili yekamva Oracle. UYise imbeko yakhe ebizwa ngokuba le nkwenkwe ngu kaPythagoras.

Nomfundisi wafunda ezingqondweni elikhulu ixesha. Phakathi Ootitshala kaPythagoras aselula Pherecydes kuvela Germodamant Sirossky. Eyokuqala wafaka kuye uthando zomculo,-bulumko yesibini wafundisa. Zombini ezi Sciences ziya kuhlala ugqaliselo zezenzululwazi kubo bonke ubomi bakhe.

Imfundo kunyaka-30-elide

Ngokutsho kuguqulelo mnye, ukuba abafana nxanelwe ulwazi, kaPythagoras washiya ilizwe lokuzalwa kwakhe. Waya kufuna ulwazi eYiputa, apho wahlala, ngokutsho kwimithombo eyahlukeneyo, ukususela kwiminyaka-11 ukuya 22, yaye emva koko wasiwa ababanjiweyo, ndithumele eBhabheli. KaPythagoras akwazi ukuxhamla kumalungiselelo ayo. Iminyaka eli-12, wafunda izibalo, geometry, kunye magic sikarhulumente yamandulo. ESamo Pythagoras akazange abuye de engama-56 ubudala. Apha, ngoxa imithetho IiPolycrates uzwilakhe. KaPythagoras ayikwazanga ukwamkela inkqubo yezopolitiko, yaye kungekudala waya ngasezantsi Italy, apho wayebekwe thanga yesiGrike Croton.

Namhlanje awukwazi uthi siqiniseke ukuba kaPythagoras waba eYiputa naseBhabhiloni. Mhlawumbi wamshiya sagaleleka eSamo, kamva waya ngoko nangoko Croton.

Pythagoreans

Imbali theorem kaPythagoras enxulumene nophuhliso okudalwe sobulumko yesiGrike esikolweni. Le abazalwana zonqulo-ethical washumayela ngqo indlela ethile, wafunda arithmetic, geometry kunye ngeenkwenkwezi, wayenza ekufundeni kwicala bulumko kunye eyimfihlakalo manani.

Bonke abafundi lokuvula sezibalo Greek yabhalwa nguye. Noko ke, imbali ngemvelaphi theorem kaPythagoras ubotshelelwe biographers yamandulo kuphela sobulumko. Kuthathwa ukuba unike amaGrike ulwazi olufundwe eBhabhiloni eYiputa. Kukho kwakhona uguqulelo ukuba ngokwenene wafumanisa ukuba theorem phezu ngokulinganayo imilenze kunye hypotenuse, engazi malunga ngempumelelo kwezinye iintlanga.

Theorem kaPythagoras: imbali amazwe

Kwezinye imithombo zamaGrike ukuchaza uvuyo bakaPythagoras, xa akwazi ukungqina theorem. Imbeko ngesi siganeko, waza wayalela idini koothixo ngohlobo amakhulu zeenkomo, waza wenza itheko. Abanye abaphengululi, ke, zalatha nakwenzeka ukwenza intshukumo enje ngenxa yemeko Pythagoreans iimbono.

Kukholelwa ukuba kwi othi "Elements", wadala yi Euclid, umbhali unika ubungqina theorem, nombhali apho sezibalo enkulu yamaGrike. Noko ke, le mbono ayixhaswanga bonke. Ngoko ke, nkqu sobulumko yamandulo Neoplatonist Proclus wabonisa ukuba umbhali oku kungentla kwi "Principia" ngokwaso ubungqina Euclid.

Nantoni na, kodwa owokuqala nokucacisa theorem ukuba yayingekho Pythagoras.

Egypt yamandulo neBhabhiloni

theorem kaPythagoras, esingethe umbandela ibali indalo kweli nqaku, ngokutsho sezibalo German Cantor, yayibizwa ngokuba kwangethuba 2300 BC. e. eYiputa. Abemi bamandulo wolawulo kwiNtlambo umNayile uFaro Amenemhat Ndandisazi equity Februwari ³ + 4 = 5 ^{² ².} Kuthathwa ukuba ngoncedo unxantathu macala 3, 4 no-5 ka umYiputa "intambo natyagivateli 'emgceni iiengile.

Eyaziwa theorem bakaPythagoras eBhabhiloni. Kumacwecwe odongwe uthandana ukususela ku-2000 BC attributed ebukumkanini uKumkani uHammurabi, wafumanisa ukuba ubalo omalunga le hypotenuse kanxantathu tye.

India neChina

Imbali theorem kaPythagoras edibene impucuko amandulo Indiya kunye neTshayina. Othi "Xuan Zhou bi-jin" iqulethe imiyalelo unxantathu zaseYiputa (emacaleni aso zinxulumene njengoko 3: 4: 5) iye yaziwa China kwasekuqaleni kwi XII. BC. e. nakuyo VI. BC. e. imathematika kule meko ukwazi uhlobo jikelele theorem.

Ukwakhiwa isibiyeli triangle ilungelo usebenzisa umYiputa kuchazwa Indian othi "Sulva Sutra" ezisukela VII-V cc. BC. e.

Ngoko ke, imbali theorem kaPythagoras kwixesha lokuzalwa sezibalo yamaGrike sobulumko uhamba emva kweminyaka engamakhulu aliqela.

ubungqina

Ngexesha theorem yayo ubukho wayengomnye geometry ngxabano. Imbali ubungqina theorem bakaPythagoras, mhlawumbi kwaqala kuqwalaselo alinganayo unxantathu ekunene. On hypotenuse yayo kunye namacala zakhiwa izikwere. Lowo "wakhula" phezu hypotenuse, uya kuba oonxantathu ezine bayalingana ukuya kowokuqala. Le nezikwere cathetus ngaloo luqulathe oonxantathu ezimbini. ukumelwa Simple graphic ibonisa ngokucacileyo semthethweni ngoluvo kwenziwa ekwimo theorem odumileyo.

Obunye ubungqina elula ngokudibanisa geometry sezibalo. oonxantathu ekunene-engile egqithe ezine twatse enamacala a, b, c basondela ukwenzela ukwenza izikwere ezimbini: Kwicala elingaphandle kunye (a c +) kunye icala ngaphakathi kunye. Ngaloo indawo encinci ye sigcawu ezilinganayo ^ezi-2. Le ndawo ye abaliweyo enkulu kwisixa se iindawo ngcambu encinane kunye bonke oonxantathu (indawo olubuxande kwicala lwe nxantathu, sikhumbula, ebalwa yi kwifomula (A * B) / 2), okt ² + 4 * ((A * B) / 2), nto leyo ilingana ² + 2av. Ummandla isikwere enkulu kubalwa ngendlela eyahlukileyo - njengoko imveliso macala mabini, oko kukuthi, (a + b) ^2, nto leyo ilingana ² + ² + 2av. Kuvela:

kunye 2av + ² + ² + ² = 2av,

² + ² = s ^2.

Kukho ezahlukeneyo ezininzi ukucikideka le theorem. Ngaphezu nabo babesebenza kunye Euclid, kunye oosonzululwazi Indiya, kunye noLeonardo da Vinci. Kudla zo yamandulo zakhokelela imizobo, imizekelo apho ibekwe ngasentla kwaye musa ukunika nayiphi na ingcaciso, ngaphandle amanqaku, "Khangela!" Ukuba lula bobungqina zejiyometri ukuba kukho ezinye izimvo nolwazi yaye akazange afune.

Imbali theorem kaPythagoras, kushwankathelwa zibe nqaku iphelisa intsomi malunga imvelaphi yayo. Noko ke, kunzima ukucinga ukuba igama sezibalo enkulu yamaGrike sobulumko nanini kuyeka ukuba ezinxulumene nayo.