Pascal's triangle

Pascal's triangle

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Credit: ROBERT BROOK/SCIENCE PHOTO LIBRARY

Caption: Ancient number series forming a triangle where each row down contains the sum of adjacent numbers above, and there ca n be any number of rows. Although attributed to Blaise Pascal, there are records of its use in much older cultures in China, India and Iran (then Persia), and it possibly dates back to the Indian mathematician Pingala in approximately 200 BC. One of the main properties of the series is that it is a list of binomial coefficients, that is the numbers that are multiplied with the variables when binomial expressions are expanded. Other properties of the triangle are the various number series and patterns contained within it such as triangular numbers in the third diagonal, increasing exponents of 11 represented by each line, Fibonacci sequence derived from repeated sums of stepped diagonals, as well as sequences for calculating probability. Computer artwork.

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