Famous numbers on a Chessboard

  • Johannes W. Meijer

Resumen

In this article it is shown how famous numbers like Pascal’s triangle, the Fibonacci
numbers, Catalan’s triangle, Delannoy’s square array, the Pell numbers and Schröder’s
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.

Publicado
2010-12-01
Sección
Artículos de Investigación