Fibonacci Sequence
The Fibonacci sequence is a series where each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... The ratio of consecutive Fibonacci numbers approaches the golden ratio φ ≈ 1.618.
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Pro Tip
Any three consecutive Fibonacci numbers form a Pythagorean-like identity: F(n)² + F(n)×F(n+1) + F(n+1)² = F(2n+1). Also: the last digit of Fibonacci numbers repeats with period 60 (Pisano period).
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Did You Know?
The sequence was introduced to Europe by Leonardo of Pisa ('Fibonacci') in 1202 via his book Liber Abaci, through a rabbit breeding problem. However, Indian mathematicians Virahanka and Hemachandra had described the sequence centuries earlier.
References
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