Definition:Wythoff Pair

Definition

A Wythoff pair is an ordered pair of integers of the form:

$\tuple {\floor {k \phi}, \floor {k \phi^2} }$

where:

$\phi$ denotes the golden section: $\phi = 1 \cdotp 618 \ldots$

$\floor x$ denotes the floor of $x$

$k$ signifies a positive integer: $k \in \Z_{\ge 0}$.

Thus the coordinates of a Wythoff pair are corresponding terms of the lower and upper Wythoff sequences.

Source of Name

This entry was named for Willem Abraham Wythoff.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$