"Euclid: The Game" is, as its name suggests, a game inspired by the constructive principles of Euclidean Geometry. It is also, as its name might not suggest, highly addictive, even for non-mathy types.

The game, which you can play here, was created with java in the open-source geometry package GeoGebra by Kasper Peulen. **(Update: Peulen has stopped by in the comments to field questions about his game.)** Its premise is simple: Players are presented a geometric puzzle in the form of a task. The first level, for example, asks the player to construct an equilateral triangle from the line segment AB:

To achieve this initial task, the player is provided a virtual compass (for drawing circles) and ruler (for generating line segments and rays). The successful completion of this and future tasks unlocks new geometric principles that can be used to solve later puzzles. In this way, the player's toolset grows as she progresses through the game's 20 levels, building upon itself in a manner reminiscent of Euclid's own deductive methods.

You don't need to be a math whiz to enjoy the game. It requires a basic familiarity with geometric shapes, but most concepts (What is an equilateral triangle?, What does "bisect" mean?, etc.) are explained as they are introduced. A familiarity with Euclid's constructive proofs, as presented in his mathematical treatise, *Elements*, will certainly make things easier, but is by no means necessary. The solution to the game's first level, for example, is based on the proof on the left, which appears in *Elements*. The intersection of two circles with radii equal to the length of a given line segment, and centered on either end of that segment, can serve as the third vertex of an equilateral triangle that includes the segment as one of its sides.

The puzzles build from there. All-in-all, it's one of the more educational time-sucks we've encountered in some time.

H/t Jesse Galef

## DISCUSSION

It's funny that this is a game. I had to use GeoGebra extensively during my Masters program to work out a lot of the geometry theorems. So, to see this put forward as a game, I have to wonder if the people involved used GeoGebra in their graduate programs as well and just decided to make their files available for the general public.