The recent discovery of a metallic alloy that behaves like a crystal, but which is characterized by a ‘forbidden’ fivefold or icosahedral symmetry, has led to the redefinition of the crystalline state. These ‘quasi-crystals’ have since become the subject of intense study and debate. In this paper we describe the remarkable properties of quasicrystals and show how their structure can be described with the aid of concepts developed in other disciplines: the golden number, Penrose tiling, and the theory of irrational numbers.