Wythoff array: Difference between revisions

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{{short description|Infinite matrix of integers derived from the Fibonacci sequence}}

In mathematics, the '''Wythoff array''' is an infinite [[Matrix (mathematics)|matrix]] of [[integer]]s derived from the [[Fibonacci sequence]] and named after Dutch mathematician [[Willem Abraham Wythoff]]. It was first defined by {{harvtxt|Morrison|1980}} using Wythoff pairs, the coordinates of winning positions in [[Wythoff's game]]; it can also be defined using [[Fibonacci number]]s and [[Zeckendorf's theorem]], or directly from the [[golden ratio]] and the [[recurrence relation]] defining the Fibonacci numbers. 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.

The Wythoff array was first defined by {{harvtxt|Morrison|1980}} using Wythoff pairs, the coordinates of winning positions in [[Wythoff's game]]. It can also be defined using [[Fibonacci number]]s and [[Zeckendorf's theorem]], or directly from the [[golden ratio]] and the [[recurrence relation]] defining the Fibonacci numbers.

==Values==