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Pascal's triangle appeared in some work by the Indian mathematician Pingala in the 2nd Century BC. Although details of Pingala's work are lost, the idea was subsequently expanded upon by Halayudha in the tenth Century. At around the same time, it was discussed by the Persian mathematician, Al-Karaji. It was also known to the Chinese mathematician Jia Xian in the eleventh Century. It is quite possible that the underlying combinatorial mathematics was known to earlier mathematicians but in any case, it is abundantly clear that Pascal was too late by over 3.5 Centuries. It says something about the Eurocentric writers that it is called Pascal's triangle, doesn't it?
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What is Binomial Expansion and how does it relate to Pascal's Triangle?
The binomial expansion is the expanded form of the algebraic expression of the form (a + b)^n.There are slightly different versions of Pascal's triangle, but assuming the first row is "1 1", then for positive integer values of n, the expansion of (a+b)^n uses the nth row of Pascals triangle. If the terms in the nth row are p1, p2, p3, ... p(n+1) then the binomial expansion isp1*a^n + p2*a^(n-1)*b + p3*a^(n-2)*b^2 + ... + pr*a^(n+1-r)*b^(r-1) + ... + pn*a*b^(n-1) + p(n+1)*b^n
What are the multiples of 5 within pascals triangle?
The Sierpinski Triangle
Who discovered pascals triangle?
Omar Khayyam discovered Pascal's triangle.
What is the sum of the numbers in the 5th row of pascals triangle?
depends. If you start Pascals triangle with (1) or (1,1). The fifth row with then either be (1,4,6,4,1) or (1,5,10,10,5,1). The sums of which are respectively 16 and 32.
Did pascals triangle or fibonaccis sequence come first?
Fibonacci lived about 400 years before Pascal did.
