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Blaise Pascal
"Among the contemporaries of Descartes none
displayed greater natural genius than Pascal, but his mathematical reputation
rests more on what he might have done than on what he actually effected,
as during a considerable part of his life he deemed it his duty to devote
his whole time to religious exercises."
Blaise Pascal was born in Clermont, France on June 19, 1623, and died in Paris, France on Aug. 19, 1662. Pascal’s father was a local judge at Clermont, and moved to Paris in 1631. In 1653 he had to administer to his father's estate. He now took up his old life again,and made several experiments on the pressure exerted by gases and liquids. Also in 1653, Pascal employed his TRIANGLE , but no account of his method was printed until 1665.
Pascal's triangle is constructed by each horizontal line being formed from the line above it. Each individual number is the sum of the two numbers immediately above it to the left and right. You have to imagine there is a "0" to the left of the left side of the triangle and a "0" to the right of the right side of the triangle. For example, the 9 (in blue) was formed by adding the 1 and 8 from the line above. The 36 (in blue) was formed by adding the 8 and 28 from the line above.
The hockey stick pattern (purple) is used to show the sum of the numbers along the diagonal. The sum of the right-facing diagonal 1 + 3 + 6 + 10 is found by going to the left at the end of the diagonal to find the number 20. If you were to follow a left diagonal, the answer would be found by switching to the right at the end. Here is an example of the hockey pattern in the triangle:
Here is an other example of Pascal's Triangle:
The area inside the outline of a triangle is the first five lines of the triangle.
Pascal's triangle can also show a Fibonacci sequence.