Polygonal Number - Formula

Formula

If s is the number of sides in a polygon, the formula for the nth s-gonal number P(s,n) is

The nth s-gonal number is also related to the triangular numbers Tn as follows:

Thus:

For a given s-gonal number P(s,n) = x, one can find n by

Read more about this topic:  Polygonal Number

Famous quotes containing the word formula:

    I cannot give you the formula for success, but I can give you the formula for failure—which is: Try to please everybody.
    Herbert B. Swope (1882–1958)

    Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.
    Pierre Simon De Laplace (1749–1827)

    Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.
    Walter Pater (1839–1894)