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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.
What does pascals triangle relate the coefficients to?
Expansion of the Binomial a+b
How is the pascal triangle and the binomial expansion related?
If the top row of Pascal's triangle is "1 1", then the nth row of Pascals triangle consists of the coefficients of x in the expansion of (1 + x)n.
What is another name for pascals triangle?
The expanded binomial is another name for Pascal's triangle.
When was pascals triangle discovered?
in the 11th century...
What are the possibilaties of Pascals Triangle?
to find out the coefficent for binomial expression, to check values like nCr
What are some cool fact on pascals triangle?
Pascal's triangle is a triangular array where each number is the sum of the two numbers above it. The numbers in the triangle have many interesting patterns and relationships, such as the Fibonacci sequence appearing diagonally. Additionally, the coefficients of the binomial expansion can be found in Pascal's triangle, making it a useful tool in combinatorics and probability.
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 fields of mathematics uses pascals triangle?
Pascal's Triangle is used in various fields of mathematics, including combinatorics, algebra, and number theory. In combinatorics, it provides a convenient way to calculate binomial coefficients, which are essential in counting combinations. In algebra, it aids in expanding binomial expressions through the Binomial Theorem. Additionally, it has connections to probability theory, such as in calculating probabilities in binomial distributions.
Examples of Pascals triangle?
Pascal's triangle
Who discovered Pascals triangle before pascal?
It was discovered first by a Persian Mathematician named Al-Karaji, then followed by numerous other people from places such as China.
Who first named the triangle pascals triangle?
pascal
What is the 6 line in pascals triangle?
The 6th line in Pascal's Triangle corresponds to the coefficients of the binomial expansion of ((a + b)^6). It is represented as: (1, 6, 15, 20, 15, 6, 1). Each number is derived from the sum of the two numbers directly above it in the previous row. The entire 6th line can be indexed starting from 0, so it is often referred to as the 7th row.
