Blog 2 - Current Event

Recently, I saw an article posted on io9 titled Try Your Hand At This Ridiculously Addictive Geometry Game. The title wasn't very descriptive and, in fact, seemed like clickbait, but the preview image was one of Euclid's geometric proofs, so I decided to give it a shot.

It turns out this article was about a game called Euclid The Game, which was written by second-year mathematics student, Kasper Peulen. In this post on Stack Exchange, he explains that he was inspired to create the game by watching a video about Euclid's Elements. The way he describes it, in a video game, you start off with a few basic abilities, but as time goes on, you unlock bigger and more powerful ones that allow you to do cooler and flashier things. As he was learning about Euclid's Elements, he couldn't help but feel like it was the same thing happening.

Elements is a collection of geometric proofs compiled by the Greek mathematician Euclid. It starts off with a series of definitions (things like "An acute angle is an angle less than a right angle."), postulates (things like "you can draw a circle given its centerpoint and radius"), and common notions (things like "Things which equal the same thing also equal one another."). Given these, he then describes a series of propositions (things like "you can construct an equilateral triangle with a side of any given line segment". The propositions are accompanied by geometric proofs that show how you can complete the action with only the given postulates and common notions. In Euclid The Game, these postulates provide the moveset and the propositions provide the levels.

If that sounds a bit complicated, let's take an example. Level 1 of Euclid The Game uses the proposition I mentioned above, constructing an equilateral triangle. In Elements, the proof that accompanies this proposition looks like the image to the right. You start with line segment AB and have to create triangle ABC. We know that any point on a circle is the same distance away from the center as any other point on the circle. We can use this to find an equilateral triangle because if we make a circle starting at A with radius AB and another starting at B with radius AB, we know that when they intersect, that point is just as far away from B as it is from A, and that that distance is how far apart A and B are from each other. Now, this description is very wordy and kind of hard to follow even if you know the mathematical principles behind it. I could easily describe it to a mathematician using formal proofs, but those aren't very interesting to read even to mathematicians, let alone to students. However, looking at the geometric proof presented, the concept is pretty clear. When you play Euclid The Game, you get to play around with these postulates and really explore how they hold true. You create the geometric proofs instead of just reading about them and, honestly, if you're anything like me, you'll have a lot of fun trying to solve the puzzle.

There are 20 levels to the game, so give it a try. Let me know what you think! Did you have fun? What levels did you think were hard? Do you feel more interested in geometry than you did beforehand? I got stuck at level 19, so let me know how far you got in the comments!