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Acta Nova
versão impressa ISSN 1683-0789
Resumo
MEIJER, Johannes W. Famous numbers on a Chessboard. RevActaNova. [online]. 2010, vol.4, n.4, pp. 589-598. ISSN 1683-0789.
In this article it is shown how famous numbers like Pascals triangle, the Fibonacci numbers, Catalans triangle, Delannoys square array, the Pell numbers and Schröders triangle can be constructed on a chessboard with a rook, knight, bishop, king or queen. Furthermore, several new triangle sums, which are all named after chess pieces that are leapers and add up numbers according to the way they leap, are introduced. Finally a new theory of how Hipparchus, who lived around 150 BC, might have calculated his two famous numbers with the aid of a chessboard is presented.