This mathematical concept is demonstrated on the Galton board, on which it determines the number of 
This mathematical concept is demonstrated on the Galton board, on which it determines the number of paths a ball can take to reach a peg. A fractal can be created from this construct by only displaying it's odd numbers. That fractal was developed by Sierpinski. It's first diagonal is useless, but it's other right-to-left diagonals display well known mathematical series. One of these series is composed of the triangular numbers. It is useful for displaying the coefficients of a binomial expansion, in which the row number displays the coefficients of binomial x+y raised to that row's number. For ten points, name this geometric construct whose namesake is that of a French Mathematician.