DescriptionA tiling is a way to partition the infinite 2D plane using many copies of a few shapes. Ordinary tilings are periodic; they repeat themselves. This is how we know a tiling could cover the plane, although we can only see a finite part of it.Penrose tilings, on the other hand, do not repeat in a regular way. But if we define carefully how to construct them (and there are very different ways to do this) we can still be sure that they extend to cover the plane, and we can still find different kinds of regularities and repetitions; for example, Penrose tilings are self-similar, like fractals. The golden ratio, and the Fibonacci numbers, are quite important in the shapes and processes involved, so you may be looking into their definitions, properties, and connections between the two. There are also analogues to Penrose tilings in 1D (the golden string) and in 3D (quasicrystals). This topic is suitable for several students.
PrerequisitesNo particular topic in maths beyond 1H level is required. (You may find yourself working with complex numbers and/or continued fractions.)Resources
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