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Blaise Pascal (June 19, 1623 - August 19, 1662), a French mathematician, physicist, inventor, philosopher and writer.
Its derivation goes back to Pythagoras' figurative numbers and various forms of the triangle were 'discovered' by Chinese, Arabic and Hindu mathematicians. Pascal collected together this previous work in a treatise and applied it to problems in probability theory. The triangle was subsequently named after him (after his death, I believe).
I believe that he did really 'discover' the 3-D version, Pascal's Pyramid.
What else can I help you with?
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.
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 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.
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.
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.
Examples of Pascals triangle?
Pascal's triangle
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.
