Page 379 - PowerPoint Presentation

PITAGORINA TEOREMA I NJENA PRIMENA. PYTHAGOREAN THEOREM AND ITS APPLICATION

AUTOR: Nataša Karadţov VII razred OŠ “Starina Novak”

MENTOR: Vesna Rajšić Profesor matematike ETŠ “Nikola Tesla”

Rezime

Pitagorina teorema je dubok i višesmislen stav geometrije koji do nas dopire iz daleke prošlosti. Vekovima je sluţila kao
inspiracija za nove matematiĉke dokaze, koje su pronalazili i ljudi koji nisu bili profesionalni matematiĉari. U radu je

opisana Pitagorina teorema, njeno numeriĉko i geometrijsko znaĉenje, dokazi teoreme kao i njena primena u nekim

oblastima. U prvom delu istraţivanja dat je istorijat Pitagorine teoreme, kao i dokazi koji je potvĊuju. Za dokazivanje
teoreme korišćene su dve vrste dokaza: dokaz pomoću razloţive jednakosti i dokaz pomoću dopunske jednakosti, Euklid

(1).
U radu je objašnjena i pokazana primena Pitagorine teoreme na kvadrat i jednakostraniĉni trougao, kao i konstrukcija

nekih iracionalnih brojeva.
Pitagorina teorema i njoj obratni stav moţe se naći na samom kraju prve knjige Euklidovih Elemenata. Kako se svaka od

trinaest knjiga ovog dela završava nekim od veoma znaĉajnih stavova geometrije onog vremena, krunisanjem prve

knjige Elemenata Pitagorinim stavom, Euklid je ovu teoremu postavio na prvo mesto u geometriji.

Kljuĉne reĉi Pitagora, Euklid, pravougli trougao, teorema, dokaz, hipotenuza.

Summary

Pythagorean theorem is an old law of geometry dating from the ancient times. For many centuries it has been the
inspiration for new mathematical proofs discovered by people who were not always professional mathematicians. In this

work Pythagorean theorem is explained as well as its algebric and geometrical meaning, proofs of the theorem and its
application in certain fields of science. In the first part of this work the historical background of the teorem was

exploited and some of its proofs. To prove the theorem two different kinds of proofs were used; the proof by separable

equations and the proof by additional equations. Euklid (1).
The application of Pythagorean theorem to squares and equilateral triangles and the construction of some irrational

numbers have also been explained. Pythagorean theorem and the converse of the theorem can be found at the end of
Euclid‟s Elements, Book (1). As each of thirteen books of Elements is concluded with some very important laws of

geometry of that time, the fact that Euclid finished his first book with Pythagorean theorem gives it a special
significance as being the basic law in geometry.

Kay words Pythagoras, Euclid, right triangle, theorem, proof, hypotenuse
.