‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture

One of the oldest and simplest problems in geometry has caught mathematicians off guard — and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire plane without gaps or overlaps. And yet, “not a lot has been known until fairly recent times,” said Alex Iosevich, a mathematician at the University of Rochester. The most obvious tilings repeat: It’…

Source