Fibonacci sequence
Videos
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
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.
Golden ratio
Videos
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a
Fibonacci sequence
…an artichoke, and the arrangement of a pine cone's bracts, though they do not occur in all species. Fibonacci numbers are also strongly related to the golden ratio: Binet's formula expresses the n-th Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers…
Michael Maestlin, the first to write a decimal approximation of the ratio
Dan Shechtman demonstrates quasicrystals at the NIST in 1985 using a Zometoy model.
Da Vinci's illustration of a dodecahedron from Pacioli's Divina proportione (1509)
Detail of the saucer plant, Aeonium tabuliforme, showing the multiple spiral arrangement (parastichy)