Talesovi teoremi

Abstract

Talesovi su teoremi jedno od važnijih postignuća elementarne geometrije. Postoje razni dokazi ovih teorema, ali ni za jedan nije sigurno da je izvorni, tj. da ga je upravo u tom obliku izrekao Tales. Teoremi se javljaju na svim razinama obrazovanja, od osnovnoškolske do fakultetske. Osim sto njihovom primjenom možemo riješiti razne matematičke probleme i zadatke, možemo riješiti i razne probleme iz realnog života, kao što je i opisano u radu. U prvom smo dijelu naveli biografske podatke o Talesu, o njegovom doprinosu matematici i utjecaju na znanstvenike koji su živjeli nakon njega. Dokaze Talesovih teorema, krenuvši od teorema u njihovom prvotnom obliku, do iskaza i dokaza kakve danas poznajemo, smo opisali u drugom poglavlju. Konačno, u trećem smo poglavlju povezali Talesove teoreme i osnovnoškolsku te srednjoškolsku razinu obrazovanja i naveli razne primjere koji se rješavaju primjenom Talesovih teorema.Tales theorems are one of the most important discoveries of elementary geometry. There are various proofs of these theorems, but none of these proofs were never found to be said by Tales himself. Theorems are represented in all levels of education, from Elementary school to Colleges. Except that their application can solve various mathematical problems and tasks, we can solve a variety of problems in real life also, as we describe in this paper. First chapter contains general, biographic information about Tales, his contribution to mathematic and his influence on scientists years after his death. Proofs of Tales theorems, starting from theorems in their original form to statements and evidences as we know today are described in second chapter. Finally, in the third chapter, we connected Tales theorems with primary and secondary level of education. Also, we have selected a various examples which can be solved using Tales theorems