Pascal's triangle
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In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world
Pascal's version of the triangle
Fibonacci sequence
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In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci number
Pascal's triangle
…probabilities of winning the various prizes. If the rows of Pascal's triangle are left-justified, the diagonal bands (colour-coded below) sum to the Fibonacci numbers. Due to its simple construction by factorials, a very basic representation of Pascal's triangle in terms of the matrix exponential can be given: Pascal's…
A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) 13 entries of the Fibonacci sequence: the indices from present to XII (months) as Latin ordinals and Roman numerals and the numbers (of rabbit pairs) as Hindu-Arabic numerals starting with 1, 2, 3, 5 and ending with 377.