Page 380 - PowerPoint Presentation

PITAGORINA TEOREMA – DOKAZI. PYTHAGORA'S THEOREM – PROOFS

AUTOR : LUKA ŢIVKOVIĆ , VII6 , O.Š. "Branko Ćopić" Beograd

NASTAVNIK : SLAĐANA KOSAĈEVIĆ ,nast.mat. O.Š. "Branko Ćopić" Beograd

MENTOR : VESNA RAJŠIĆ , prof. matematike, E.T.Š "Nikola Tesla" Beograd

REZIME

Pitagorina teorema je pojam u geometriji koji definiše odnos izmeĊu tri stranice pravouglog trougla. Ime je dobila po

starogrĉkom matematiĉaru Pitagori koji je ţiveo u 6. veku p.n.e. On je iskoristio saznanja mnogih naucnika koji su ţiveli

pre njega, i saţeto ih izrazio u stavu : Površina kvadrata nad hipotenuzom, je jednaka zbiru površina nad katetama, a
zatim je to matematiĉkim putem i dokazao. Ova saznanja bila su poznata još vavilonskim, kineskim, indijskim i

egipatskim nauĉnicima mnogo vekova ranije. Ipak, starogrĉka matematika je bogatija i svestranija od dotadašnjih nauka
jer je teţila ka tome da se sva saznanja dokaţu i obrazloţe na nauĉni naĉin. Prvi poznati pisani dokaz Pitagorine

teoreme nalazi se u Euklidovim Elementima . Ova teorema je bila inspiracija mnogim nauĉnicima kroz vekove, sve do
današnjih dana. Na razne naĉine izvoĊeni su dokazi koji su vodili ka novim korisnim i zanimljivim zakljuĉcima.

Ključne reči : Pitagorina teorema, pravougli trougao, hipotenuza, katete, iracionalni brojevi ,Pitagorine trojke,

Pitagorino drvo.

SUMMARY

Pythagorean theorem is a concept in geometry which defines relationship between three sides of a right triangle. The

name was given by ancient Greek mathematician Pythagora, who had lived in 6.century BC. He used knowledges of
many scientists who lived before him, and summarized them , pointed in proposition: The square of the hypotenuse of a

right triangle is equal to the sum of the squares on the other two sides. Theese findings were known to Babylonian,

Chinese, Indian, Egyptian scientists meny centuries before. However, mathematic of the ancient Greeks is more richfull
and versatile from former sciences because it was streaming for prooving all findings and scientificaly explaines.

First known written proof of Pythagorean theorem was found in Euclids Elements . Theese theorem was inspiration for
many scientists through centuries, allthrough nowadays. Proofs were taken in many diferent ways which led to new useful

and interesting conclusions.

Key words : Pythagorean theorem, right triangle , hypotenuse, catheti, irrational numbers, Pythagorean triple, Pythagoras
tree.