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 feel like a white granular mass of amorphous crystals—my formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,—with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.
    Lafcadio Hearn (1850–1904)

    “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)

    But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the formula for that? The formula for that is not included in the curriculum.
    Fannie Hurst (1889–1968)