  In this paper, we introduce a new generalization of Pascal's triangle. The
new object is called the hyperbolic Pascal triangle since the mathematical
background goes back to regular mosaics on the hyperbolic plane. We describe
precisely the procedure of how to obtain a given type of hyperbolic Pascal
triangle from a mosaic. Then we study certain quantitative properties such as
the number, the sum, and the alternating sum of the elements of a row.
Moreover, the pattern of the rows, and the appearence of some binary
recurrences in a fixed hyperbolic triangle are investigated.
