In this semilab, we will discuss the mathematics of patterns and tilings. What is a symmetry? How many different types of symmetry are there?
We will study symmetries of ornaments in medieval castles and Escher's drawings, classify crystals. We will also talk about the mysterious quasicrystals, patterns that are almost periodic but not quite, and share the story of their discovery in nature. We will explore Penrose tiles and the recent discovery of a monotile, a quasiperiodic tiling of the plane using only one tile.
Prerequisites: high school geometry course.