Wolfram Demonstrations Project

Numbers can be well approximated by numbers of the form

, where

and

are integers and

is irrational. This property can be used to tile a room almost perfectly, with just three tile sizes, and with no need to cut any tiles.

E. Pegg Jr and A. Fisher, "Tessellation Set", US Patent 6309716.

The numbers are Euler's number

, the golden ratio

, Pythagoras's number

, Khinchin's constant

, Euler gamma

, Glaisher's constant

, Catalan's number

, and

Contributed by: Ed Pegg Jr

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Tiling a Room Irrationally