The Fibonacci series.
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The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. Fibonacci's 1202 book Liber Abaciintroduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics.
In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression.
1, 1, 2, 3, 5, . . . is the beginning of the Fibonacci Series, the basis of the "Golden Ratio" of Greek architecture, and a whole bunch of other stuff in nature, physics, and math. The limit of the ratio of two consecutive terms in the series is the solution to (X+1) = 1/X . It's also pretty close to the number of miles in one kilometer, but that's absolutely pure and total coincidence.
In terms of mathematics, a coefficient plays the role of a multiplicative factor in a series or an expression. The two different kinds of coefficients include numbers and letters.
Turns up in many things - the leaves of a fern, the spirals in pinecones, the nautilus shell chambers etc