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:

    Every formula which expresses a law of nature is a hymn of praise to God.
    Maria Mitchell (1818–1889)

    In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the child’s age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.
    Alicia F. Lieberman (20th century)

    The formula for achieving a successful relationship is simple: you should treat all disasters as if they were trivialities but never treat a triviality as if it were a disaster.
    Quentin Crisp (b. 1908)