Gilbreathov princip s primjenama na fraktale, popločavanja i magične trikove

Posavec, Ivana (2015) Gilbreathov princip s primjenama na fraktale, popločavanja i magične trikove. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

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.

Item Type: Thesis (Diploma thesis)
Supervisor: Brückler, Franka Miriam
Date: 2015
Number of Pages: 42
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 17 Jun 2015 11:57
Last Modified: 17 Jun 2015 11:57
URI: http://digre.pmf.unizg.hr/id/eprint/4058

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