Eyvana's+Math+Fact-+Pascals+triangle

=__**Pascals Triangle!!!**__=

Pascal's triangle was fist studied by Chinese mathematician Yangui and Persian poet/ astronomer Omar Khayyam and later by B. Pascal who is it is named after. It is a number triangle with the numbers arranged in a way that the following formula can be applied:

where is a [|binomial coefficient].  the Triangle starts with n=0 and is:  [|Pascal's formula] shows that each subsequent row is obtained by adding the two entries diagonally above, [|Here is were I found this information]
 * [[image:http://mathworld.wolfram.com/images/equations/PascalsTriangle/NumberedEquation1.gif width="136" height="37" caption=" a_(nr)=(n!)/(r!(n-r)!)=(n; r), "]] || (1) ||
 * [[image:http://mathworld.wolfram.com/images/equations/PascalsTriangle/NumberedEquation2.gif width="100" height="123" caption=" 11 11  2  11  3  3  11  4  6  4  11  5  10  10  5  11  6  15  20  15  6  1 "]] || (2) ||
 * [[image:http://mathworld.wolfram.com/images/equations/PascalsTriangle/NumberedEquation3.gif width="230" height="37" caption=" (n; r)=(n!)/((n-r)!r!)=(n-1; r)+(n-1; r-1). "]] ||

Here are some more pictures of the triangle: