Can You Really Solve This Tricky Rep-Tile Puzzle?
If you are looking for a hard geometry challenge, look no further!
In 1961, American mathematician Solomon W. Golomb coined the term: Rep-Tile as a pun on “reptiles”. Golomb had been researching replicating geometrical figures and had landed upon an interesting phenomenon. He went on to publish three papers on the topic of replicating polygons. This in turn turned out to be pioneering work in this field.
In this essay, I will initially be covering the fascinating world of rep-tiles by giving a basic introduction to the topic. Following this, what awaits you is a very tricky, yet engaging puzzle. Let us begin.
What is a Rep-Tile?
The term rep-tile refers to any replicating geometrical figure that could be used to tile an entire plane without using any other shape. As an example, consider the typical square tiles. Using the same shape (a square that enjoys reflective and rotational symmetry), we would be able to tile an entire plane without needing any other shape.
As it turns out, among regular geometrical polygons (all sides equal / all angles equal), only the square, the equilateral triangle, and the regular hexagon can be used to tile an entire plane without using any other respective shapes. Among…
