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Tuesday, November 30, 2010

Pascal's Triangle and Expanding Polynomial Powers

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Note: In Pascal's Triangle, the key to figuring out a given number is to add the left and the right numbers of the row immediately above. The sum of all the numbers in each row is equivalent to 2^row#. The individual numbers in each of the rows divided by the total of the row it is in shows a probability of getting that combination of heads or tails if a coin is flipped row# of times (row1 - 1H, 1T), (row 2 - 2H, 1H1T, 2T), etc.



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Update 11/30/2010 - Here demonstrates how the Fibonacci Sequence (1,1,2,3,5,8,13,21...) is the summation of the oblique diagonals of Pascal's Triangle.