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In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two ... Fibonacci identities often can be easily proved using ...
Cassini's identity (sometimes called Simson's identity) and Catalan's identity are mathematical identities for the Fibonacci numbers. Cassini's identity, a special case of Catalan's identity, states that for the nth Fibonacci number, + = (). Note here is taken to be 0, and is taken to be 1. Catalan's identity generalizes this:
Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity; Binomial inverse theorem; Binomial identity; Brahmagupta–Fibonacci two-square identity; Candido's identity; Cassini and Catalan identities; Degen's eight-square identity; Difference of two squares; Euler's four-square identity; Euler ...
Geometric interpretation of the Candido identity for sequential Fibonacci numbers. The white area equals the grey area and each of them equals half of the outer square's area. [1] Candido's identity, named after the Italian mathematician Giacomo Candido, is an identity for real numbers.
There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis.
A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous elements (with the exception of the first elements in the sequence). The usual Fibonacci numbers are a Fibonacci sequence of order 2.
Fibonacci's identity may refer either to: the Brahmagupta–Fibonacci identity in algebra, showing that the set of all sums of two squares is closed under multiplication the Cassini and Catalan identities on Fibonacci numbers
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...