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In mathematics, the Wythoff array is an infinite matrix of positive integers derived from the Fibonacci sequence and named after Dutch mathematician Willem Abraham Wythoff. Every positive integer occurs exactly once in the array, and every integer sequence defined by the Fibonacci recurrence can be derived by shifting a row of the array.
L.E. Sigler, Leonardo Pisano Fibonacci, the book of squares. An annotated translation into modern English, Boston 1987. M. Moyon, Algèbre & Practica geometriæ en Occident médiéval latin: Abū Bakr, Fibonacci et Jean de Murs , in Pluralité de l’algèbre à la Renaissance , a cura di S. Rommevaux, M. Spiesser, M.R. Massa Esteve, Paris 2012 ...
For generalized Fibonacci sequences (satisfying the same recurrence relation, but with other initial values, e.g. the Lucas numbers) the number of occurrences of 0 per cycle is 0, 1, 2, or 4. The ratio of the Pisano period of n and the number of zeros modulo n in the cycle gives the rank of apparition or Fibonacci entry point of n.
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Fibonacci instead would write the same fraction to the left, i.e., . Fibonacci used a composite fraction notation in which a sequence of numerators and denominators shared the same fraction bar; each such term represented an additional fraction of the given numerator divided by the product of all the denominators below and to the right of it.
The Fibonacci Quarterly is available online to subscribers; on December 31, 2017, online volumes ranged from the current issue back to volume 1 (1963). Many articles in The Fibonacci Quarterly deal directly with topics that are very closely related to Fibonacci numbers , such as Lucas numbers , the golden ratio , Zeckendorf representations ...