University of Zagreb. Faculty of Science. Department of Mathematics.
Abstract
Kreativna vizualizacija, odnosno sposobnost stvaranja mentalnih slika, jedan je od važnih alata koji pomažu razumijevanju matematičkih ideja, koncepata i dokaza (tzv. "dokazi bez riječi" ili "grafički dokazi"). Jednostavan, elegantan i slikovit prikaz dokaza, posebno je pogodan radi zornosti i reduciranog teksta. Ipak, vizualni dokazi kriju u sebi zamku ukoliko im se ne pristupi kritički te nikako ne mogu zamijeniti dokaz u klasičnom smislu. Kako slikom prikazujemo brojeve veće od nule, u nekim dokazima radi se tek o nepotpunoj indukciji. Stoga, kako bi se izbjegli pogrešni zaključci, svaka vizualizacija treba biti popraćena logičkim objašnjenjem i smislenim dokazom.This work presents different visualizations that are interesting from both mathematical and pedagogical point of view. The ability to create mental images are important tool that can make understanding mathematical ideas and concepts much easier. More elegant than formal math, graphic proofs offer colorful pictures and diagrams, especially convenient for students who are not very into an abstract math. Despite the positive reactions of the students, visual proofs can easily make you think in wrong direction so visualization cannot replace the proof in a classical notation. Emphasize that in some examples there is only incomplete induction so, to be a proof, each visualization must be accompanied by mathematically logical explanation
