Pascal-like Triangles Made from a Game
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The triangle of fractions has properties that makes it very similar to Pascal's triangle: suppose two adjacent fractions in the same row are and . Then the fraction below them is , which is how the fractions and are added in the Farey sequence.
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Contributed by: Hiroshi Matsui, Toshiyuki Yamauchi, Daisuke Minematsu, and Ryohei Miyadera (September 2007)
Open content licensed under CC BY-NC-SA
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Originally this game was studied as a game of Russian roulette.
For the mathematical background see T. Hashiba, Y. Nakagawa, T. Yamauchi, H. Matsui, S. Hashiba, D. Minematsu, M. Sakaguchi, and R. Miyadera, "Pascal-like Triangles and Sierpinski-like Gaskets," Visual Mathematics: Art and Science Electronic Journal of ISIS-Symmetry [online], 9(1), 2007.
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