Vizualna matematika

master's thesis

• Title (english): Visual mathematics
• Author: Melisa Klobučarić
• Mentor: Ana Prlić (mentor)
• Committee member: Ana Prlić (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Matija Bašić (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu su prikazani slikovni i klasični dokazi nekih matematičkih tvrdnji. Naglasak je na vizualnim dokazima poznatijima pod nazivom „dokazi bez riječi“. Općenito, dokaz bez riječi je jedna ili niz slika koji pomažu čitatelju da vizualno razumije zašto je određena matematička tvrdnja točna. Istodobno, on daje ideju o tome kako bi se ta tvrdnja mogla formalno dokazati. Iako vrlo intuitivni, slikovni dokazi znaju imati nedostatke kao što su nepokrivanje svih slučajeva, manjak sistematičnosti ili naprosto pogrešna čitateljeva interpretacija. Zbog toga će se vizulani dokazi pokazati u svom punom sjaju kada je uz njih kvalitetan popratni tekst i analiza slike. Cilj ovog rada je pokazati da se formalni i vizualni dokazi nadopunjuju i da zajedno čine najinformativniju i većini najlakše shvatljivu cjelinu

Abstract (english)

In this thesis, visual and classical proofs of certain mathematical statements are presented. The emphasis is on visual proofs, more commonly known as ”proofs without words.” Generally, a proof without words consists of one or a series of images that help the reader visually understand why a specific mathematical statement is true. At the same time, it provides an idea of how that statement could be formally proven. Although very intuitive, visual proofs may have drawbacks such as not covering all cases, lacking systematicity or simply being subject to the reader’s misinterpretation. Therefore, visual proofs shine in their full glory when accompanied by a high-quality supporting text and image analysis. The goal of this paper is to demonstrate that formal and visual proofs complement each other, creating the most informative and easily understandable whole when presented together.

• Keywords: „dokazi bez riječi“; formalni i vizualni dokazi
• Language: croatian
• URN:NBN: urn:nbn:hr:217:491629
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-13 11:06:22