Gilbreathov princip s primjenama na fraktale, popločavanja i magične trikove

master's thesis

• Author: Ivana Posavec
• Mentor: Franka Miriam Bruckler (mentor)
• Committee member: Franka Miriam Bruckler (predsjednik povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Aleksandra Čižmešija (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-02-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu prikazan je relativno novi kombinatorni princip koji se naziva Gilbreathov princip. Cilj ovog rada bio je prikazati taj zanimljiv, u Hrvatskoj relativno nepoznati princip i pokušati naći primjenu istog u nastavi matematike u prirodoslovno - matematičkoj gimnaziji. Glavno značenje Gilbreathova principa je sljedeće: ako u špilu s N karata odaberemo bilo koji broj k svojstava karata, pri cemu je N višekratnik od k, te špil karata posložimo tako da se svaka uzastopna k-torka sastoji od karata koje svaka ima različito od k svojstava (u istom redoslijedu u svakoj k-torci), onda će se i nakon specifičnog miješanja karata (koje se naziva Gilbreathovo miješanje) špil sastojati od uzastopnih k-torki karata s različitim svojstvima. U ovom je radu dokazano nekoliko varijanti tog principa, opisana je primjena istog na fraktale i kvaziperiodična Penroseova popločavanja ravnine te su opisani neki od kartaških trikova u kojima se on primjenjuje.

Abstract (english)

In this thesis we described relatively new combinatorial principle which is called Gilbreath principle. The main purpose of this thesis was to show that interesting, in Croatia rather unknown principle and try to find the application of the same in high school mathematics. The main result of this principle is following: if in a deck of N cards we choose any number of k properties of cards, where N is multiple of k, and we arrange a deck of cards so that the every consecutive k-tuples consist of cards which has distinct of k properties (in the same order in every k-tuples), then after specific card shuffling (which is called Gilbreath shuffle) a deck of cards will consist of consecutive k-tuples cards with distinct properties. In this thesis we proven several variants of this principle, described the use of principle on fractals and quasiperiodic Penrose tiling of plane and we described several card tricks which are based on Gilbreath principle.

• Keywords: Gilbreathov princip; primjena Gilbreathova principa u nastavi matematike; kvaziperiodična Penroseova popločavanja ravnine; nastava matematike
• Keywords (english): Gilbreath principle; application of the Gilbreath principle in high school mathematics; quasiperiodic Penrose tiling of plane; teaching mathematics; high school; middle school
• Language: croatian
• URN:NBN: urn:nbn:hr:217:111206
• 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: 2019-01-30 11:08:50