Golden ratio
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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
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)
Fibonacci sequence
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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
Golden ratio
…that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry problems but did not observe that it was connected to the Fibonacci numbers. Luca Pacioli named his book Divina proportione (1509) after the ratio; the book, largely plagiarized from Piero della Francesca, explored its properties…
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.