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Pascal’s  Triangle and it’s  application in other subjects and real  life.

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A triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n.  It is named after the 17th-century French mathematician Blaise Pascal.

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It  is an equilateral  triangle.  It has a triangular  array of numbers and its rows are named with 0th row, 1st row, 2nd row, and so on, from the top.  The  outer two equal sides of the triangle are filled by 1 at all of the  rows . The  middle numbers of the triangle are obtained by adding two numbers above it.  By  repeating this process we will end up getting a Pascal triangle.   This  is a never ending triangle .

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Properties Each  number is the  sum  of the two numbers above it.  The  triangle is symmetric.  The diagonals going along the left and right edges contain only 1’s.   The diagonals next to the edge diagonals contain the natural numbers in order.

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The next diagonal is  the triangular  numbers.  Similarly, the next diagonals are the tetrahedral numbers or triangular pyramidal numbers.

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Pascal’s  triangle determines the coefficients which arise in binomial expansion.  Supposing  you have the binomial  (a  +  b)  and you want to raise it to a power such as 2 or 3.

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Usage of Pascal’s triangle in real life

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Probability of getting Heads or Tails  Pascal’s  triangle can show us the way how heads  and tails  can combine. This gives the probability of  any combination .  H represent  heads and T represents tails. HHHH HHHT , HHTH, HTHH,  THHH TTHH , HHTT,  HTHT, HTTH,THHT ,  THTH HTTT , THTT, TTHT,  TTTH TTTT Thus , the observed pattern is 1,4,6,4,1.  (4 th  row of the Pascal’s  triangle )

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THE END THANK YOU  DEAR TEACHER  FOR YOUR  ATTENTION

Pascal's Triangle and it's application in other subjects and real life.

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