# "Quasicrystals in Nature and in Mathematics" by Yves Meyer

D. Shechtman was awarded the 1011 Nobel prize in chemistry for the discovery of quasicrystals in Nature. D. Shechtman's seminal paper was published in 1984. It soon became clear that quasicystals had been studied
previously by mathematicians (1970, 1974). Some Penrose tilings are spectacular examples of quasicrystals. Michel Duneau, Denis Gratias, and André Katz bridged the gap between mathematics and chemistry.
The aim of this lecture is to clarify the relation between quasicrystals and pavings. The Conway pinwheel paving is an exact pavings of the plane with isometric copies of one triangle. It is not a quasicystal. We also study the role of number theory (Pisot and Salem numbers) in quasicrystals.
Quasicrystals were used as decorative patterns in medieval Islamic Art.
Art, mathematics and chemistry are reconciliated.