Mind-Boggling Math Fact #2
Mathematically speaking, there’s just a finite number of distinct geometric patterns. All Escher paintings, wallpapers, tile designs and indeed all two-dimensional, and repeating arrangements of shapes can be identified as belonging to one or another of the so-called “wallpaper groups.” And how many wallpaper groups are there? Exactly 17.
The classification of the wallpaper groups is based on how individual segments of a pattern, called unit cells, fit together. To determine how they fit, and which group they fit into, mathematicians test how they can transform the pattern and still end up with it looking like the original. They test whether they can translate it (by shifting the unit cells over one place and ending up with the same thing), rotate it, reflect the pattern across a line, or “glide reflect” it, which means reflecting it across a line and simultaneously shifting it. Based on which of those four types of “symmetries” a given pattern possesses, it can be categorized in one of the 17 groups.
Does 17 seem like a very random number of pattern possibilities? Yes. Source of article here
(Note: So, does this mean that Mathematics is the foundation of all art and design?)