Figurate numbers

(Math.)

numbers, or series of numbers, formed from any arithmetical progression in which the first term is a unit, and the difference a whole number, by taking the first term, and the sums of the first two, first three, first four, etc., as the successive terms of a new series, from which another may be formed in the same manner, and so on, the numbers in the resulting series being such that points representing them are capable of symmetrical arrangement in different geometrical figures, as triangles, squares, pentagons, etc.