# 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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