Cassini's identity and Catalan's identity are related mathematical identities concerning the Fibonacci numbers, alongside a further generalization known as Vajda's identity. Cassini's identity, which is a special case of the other two, gives a formula relating the nth Fibonacci number to its neighbors in the sequence. Cassini's identity is named for the astronomer Giovanni Domenico Cassini, and Catalan's identity for the mathematician Eugene Catalan.
Facts
StatementCassini's identity, a special case of the other two, states that for the nth Fibonacci number, F(n-1) F(n+1) - F(n)^2 = (-1)^n. 1 Classification
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Source Cassini and Catalan identities - Wikipedia
Sources
1. Cassini and Catalan identities - Wikipedia
Lead section
Cassini's identity, a special case of the other two, states that for the nth Fibonacci number,
History section
Cassini's formula was discovered in 1680 by Giovanni Domenico Cassini, then director of the Paris Observatory, and independently proven by Robert Simson (1753).
Proved By: Robert Simson, Lead
Cassini's formula was discovered in 1680 by Giovanni Domenico Cassini, then director of the Paris Observatory, and independently proven by Robert Simson (1753)
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