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:

    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)

    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)

    “It’s hard enough to adjust [to the lack of control] in the beginning,” says a corporate vice president and single mother. “But then you realize that everything keeps changing, so you never regain control. I was just learning to take care of the belly-button stump, when it fell off. I had just learned to make formula really efficiently, when Sarah stopped using it.”
    Anne C. Weisberg (20th century)