Matematički paradoksi

master's thesis

• Title (english): Mathematical paradoxes
• Author: Emina Kušec
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu opisujemo matematičke paradokse iz različitih područja matematike. Paradoks krumpira jedan je od jednostavnijih paradoksa i lako se objašnjava postotnim računom. Zenonov paradoks o Ahileju i kornjači na slikovit način nam pokazuje da suma beskonačno mnogo članova može biti konačna. Rođendanski paradoks idealan je uvod u temu vjerojatnosti, a za nešto kompetentnije učenike koji uče o uvjetnoj vjerojatnosti proučavamo i Monty Hall paradoks. Za matematičko očekivanje zaintrigirat će nas paradoks dvije kuverte, a za cikličke permutacije problem 100 zatvorenika. Na kraju računamo volumen i oplošje Gabrielovog roga pa ih pokušavamo usporediti. Svaki od navedenih paradoksa prilagodili smo nastavi matematike na određenoj razini obrazovanja i time dali ideju nastavnicima kako zainteresirati učenike za spomenuta matematička područja.

Abstract (english)

In this thesis we describe mathematical paradoxes from different areas of mathematics. The potato paradox is one of the simpler paradoxes and is easily explained by a percentage calculation. Zeno's paradox about Achilles and the tortoise visually shows us that the sum of an infinite number of parts can be finite. The birthday paradox is an ideal introduction to the topic of probability, and for somewhat more competent students learning about conditional probability, we also study the Monty Hall paradox. For mathematical expectation we will be intrigued by the paradox of two envelopes, and for cyclic permutations by the problem of 100 prisoners. Finally, we calculate the volume and area of Gabriel's horn and try to compare them. We have adapted each of these paradoxes to the teaching of mathematics at a certain level of education, thus giving teachers an idea of how to interest students in the mentioned mathematical areas.

• Keywords: paradoks krumpira; Zenonov paradoks; Ahilej i kornjača; rođendanski paradoks; Monty Hall paradoks; paradoks dvije kuverte; a; problem 100 zatvorenika
• Keywords (english): potato paradox; Zeno's paradox; Achilles and the tortoise; birthday paradox; Monty Hall Paradox; paradox of two envelopes; a; the problem of 100 prisoners
• Language: croatian
• URN:NBN: urn:nbn:hr:217:029122
• 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: 2022-09-13 12:26:05