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Encyclopedia Britannica - Main :: FAT-FLA |
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FIGURATE NUMBERS , in mathematics
series 1+1+1+ ..., i.e. n, as the nth term
series , we obtain the series 1+2+3+ . . ., the sum of n terms of which is a n . n+r. Taking this sum as the nth term
1, n, n(n+1)/2!, n(n+1) (n+2) /3!,...n(n+1) ... (n+r2)l(r 1) !. The numbers obtained by giving n any value in these expressions are of the first, second, third, . . . or rth order
Pascal treated these numbers in his Traite du triangle arith-metique (1665), using them to develop a theory of combinations and to solve problems in proba- t t t t - . , j r bility. His table is here shown pOO in its simplest form. It is to be noticed that each number is the sum of the numbers immediately above and to the left of it; and that the numbers along a line
base
column
binomial ex-pansion of (t+x)'-1, where r represents the number of units cut off. End of Article: FIGURATE NUMBERS If you wish, you can link directly to this article.
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