De tessere quinquangula: five hundred years of pentagonal tilings from Dürer to Mackay via Kepler, Escher, and Penrose

Abstract Albrecht Dürer began the mathematical study of pentagonal tilings five hundred years ago with the publication in 1525 of his textbook of mathematics Underweysung der Messung . A century later Johannes Kepler produced more elaborate and intricate pentagonal tilings. In the 20th century Maurits Escher made pentagonal tilings into art. Escher’s art–science interactions with Roger Penrose made the latter keep thinking about tilings; he made pentagonal tilings tile the plane aperiodically in 1974. And Alan Mackay built on and extended Penrose’s work to predict the existence of quasicrystals in 1981.