Visualisations in Mathematics

U ovom diplomskom radu prikazani su dokazi nekih matematičkih tvrdnji pomoću slika, preko kojih bi se učenicima u osnovnim pa i u srednjim školama mogao probuditi interes za proučavanje matematike. Počinjemo prikazivanjem brojeva preko poznatih objekata te preko duljine dužina, a zatim upoznavajući se sa popločavanjima ravnine u kojima uvodimo neke vrste poliomina, dotićemo se dokaza Teorema četiri boje. Za kraj odlazimo u tri dimenzije, odnosno rješavamo probleme koji se u ravnini čine nerješivi, no pogledamo li izvan okvira, tj. u prostoru, vrlo lako dolazimo do rješenja.In this graduate thesis, some proofs of mathematical claims are illustrated with the help of images i.e. illustrations by which students in elementary and secondary schools could awaken interest for studying and elaborating mathematics. We begin by displaying numbers by graphical elements and over lengths of segments and then getting familiar with tiling of the plane in which we introduce some types of polyominos, which leads to mentioning some parts of the Four color theorem proof. Lastly we discuss about three dimensions, apropos we solve problems which in plane seem unsolvable, but if we look out of the box, i.e. in space, we can reach the solution very eas