Multinomial Theorem - Interpretations - Generalized Pascal's Triangle

Generalized Pascal's Triangle

One can use the multinomial theorem to generalize Pascal's triangle or Pascal's pyramid to Pascal's simplex. This provides a quick way to generate a lookup table for multinomial coefficients.

The case of n = 3 can be easily drawn by hand. The case of n = 4 can be drawn with effort as a series of growing pyramids.

Read more about this topic:  Multinomial Theorem, Interpretations

Famous quotes containing the words generalized and/or pascal:

    One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.
    —H.L. (Henry Lewis)

    Thus passes away all man’s life. Men seek rest in a struggle against difficulties; and when they have conquered these, rest becomes insufferable. For we think either of the misfortunes we have or of those that threaten us.
    —Blaise Pascal (1623–1662)