Generalizacije i analogoni u geometriji

master's thesis

• Title (english): Generalizations and analogues in geometry
• Author: Sonja Časek
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Vedran Čačić (član povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Tomislav Berić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Generalizacija i analogija dva su pojma koja su usko povezana. U matematici analogija i generalizacija prvenstveno imaju ulogu u otkrivanju novih matematičkih znanja. Ako uočimo neku pravilnost, možemo generalizirati općenito na sve, međutim to ne znači da će te tvrdnje biti uvijek istinite. Neke tvrdnje slijede iz već prethodno dokazanih pa analogijom dokazujemo slične tvrdnje. U ovom radu proučavali smo geometrijske tvrdnje koje imaju analogne tvrdnje i njih smo dokazivali. U prvom dijelu rada opisali smo neka svojstva trokuta i ta svojstva proširili na analogon trokutu u stereometriji koji je tetraedar. Osim trokuta proučavali smo i neka svojstva četverokuta koja smo opisali u drugom dijelu rada.

Abstract (english)

Generalization and analogy are two concepts which are closely related. In mathematics, they are being used to shorten the process of proof. It is not always necessary to prove everything. If we notice some regularities, we can generalize them in several directions, however this does not mean that these claims will always be true. Some claims follow from previously proven, so by analogy we prove similar claims. In this paper we studied geometric statements that have analogue statements and we have proven them. In the first part of the paper we described some properties of the triangle and extended these properties to the analogue of a triangle in the stereometry that is a tetrahedron. In addition to the triangle, we studied some of the properties of the quadrangle that we described in the second part of the work.

• Keywords: nova matematička znanja; geometrijske tvrdnje; analogne tvrdnje
• Keywords (english): process of proof; geometric statements; analogue statements
• Language: croatian
• URN:NBN: urn:nbn:hr:217:575639
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-10-26 07:53:22