IJPAM: Volume 85, No. 1 (2013)


Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN

Abstract. Place elements in the form of an inverted triangle, and color them from top to bottom by row according to some rule. When doing so, is it possible to predict the color of the element that becomes the triangle's bottom vertex? It turns out that when you begin with a triangle of 4, 10, 28, c elements in its top row, knowing the colors of that row's leftmost and rightmost elements is sufficient to predict the color of that bottom vertex, and this article presents an elegant proof of this surprising result. Coloring triangles is simple even for children, but this problem provides a springboard to learning about some advanced mathematics, including Abelian groups, the superposition principle, and fractal structures.

Received: December 21, 2012

AMS Subject Classification: 00A08, 20K01, 26B40, 28A80

Key Words and Phrases: congruence, Abelian group, superposition principle, fractal

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DOI: 10.12732/ijpam.v85i1.6 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 1