Tiling a Room Irrationally
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 .