PASCALS TRIANGLE

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PASCALS TRIANGLE
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Heres an array of numbers which dates back to
the Chinese around 1050
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Blaise Pascal (1623-1662) was given credit as
the first person to investigate the numerical
patterns contained in the array of numbers, hence
the name Pascals Triangle.
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Interesting Features of Pascals Triangle

• Sum of elements of the nth row 2N
• If the first number in a row, excluding the 1s,
  is prime, then all the numbers in the row are
  divisible by the number
• (Example 1 7 21 35 35 21 7 1)
• To find the rth element in the nth row, use the
  formula
• Does this look familiar?

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AKA The Binomial Triangle

• Represents the coefficients of the binomial (x
  y)n such that n 0,1,2,3,4,
• The coefficient of xryn-r in the expansion of (x
  y)n is C(n, r)

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The triangle contains the square numbers 
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The triangle contains the triangular numbers
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• If a diagonal of any length is selected starting
  at any of the 1s bordering the sides of the
  triangle and ending on any number inside the
  triangle on that diagonal, the sum of the numbers
  inside the selection is equal to the number below
  the end of the selection that is not on the same
  diagonal itself-hockey stick

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And theres more!

• There are many other fascinating aspects of
  Pascals triangle, such as points on a circle,
  fibonaccis sequence, magic 11s, and
  polygonal numbers.
• www.ptri1.tripod.com
• www.math.umt.edu/street/binomial.html
• www.cs.washington.edu/homes/jbear/classes/blaise/b
  laise.html