Viviani's Theorem

U ovom završnom radu se razmatra tvrdnja poznata u literaturi kao Vivianijev teorem koji kaže da je u jednakostraničnom trokutu suma udaljenosti bilo koje točke trokuta od stranica trokuta neovisna o izboru točke i jednaka je visini tog trokuta. Dano je nekoliko različitih dokaza teorema te navedena poopćenja i prostorni analogon teorema.In this paper, it is presented the statement known in the literature as Viviani’s theorem which says that in equilateral triangle the sum of the distances from any interior point to the sides of a triangle is independent of choosing the point. Some proofs of the theorem, the generalizations and the spatial analogue of the theorem are given