Update (6/19/2014) $\;$ Just wanted to say that this idea that I posted more than a year ago, has now become reality at: http://euclidthegame.com/
12.292 users have played it in 96 different countries, and 1232 people have reached level 20 :)
Update (8/27/2015) $\;$ The game is now played by more than 500.000 people in 213 different countries :D The iOS version is coming in september, see the facebook page.
I just watched this video about Euclid's treatise the Elements. I got introduced to the postulates and a couple of propositions of book I. I really liked this video, I'm not sure if this is because of Euclid or because of how Wildberger explains it (or maybe both ). This may sounds a little strange, especially for the mathematicians here from an older generations (I'm 22), but this way Euclid has structured his postulates/propositions reminds me to and old addiction from me: Video Games.
For the ones that are not familiar with video games: In many games you begin with some kind of character, which has some basic "abilities", for example you are able to do some kind of "fight combo", or "build" something or whatever. Okay, I may not do a good job explaining this, but I guess most here understand what I mean.
If you proceed through the different levels, you begin to get more and more abilities. In the beginning your character can only do the basics. But if you accomplish the right "goals", you character will be able "unlock" "abilities". After a while you will feel awesome about all the things your character is able to do.
When I was watching this video, I feel like, "hey, isn't that the same thing as Euclid was doing?". You begin with just 3 constructions (your begin set of abilities). And if you prove theorems (accomplish levels), you will be able to use those in new theorems (abilities you can use in new levels).
It seems like Euclid's the Elements got all the elements to be a very addictive game. I'm a little bit fancying this idea. I really see myself getting addictive to such kind of game that would guide level by level to the whole work of Euclid:
This is how I picture such a game could look like. Please forgive me for my ugly drawings.
Well, I've been looking if something like this already exist, but I couldn't find anything. So that is my first question: "Does there exist a "game" like this ?" I've seen many geometry software (like GeoGebra), and I think this excellent software, but what I would like is something that is more closer to the addictive set up of most games. Getting a character, and working your way through the levels (in this case: beginning with some basic construction and working your way through all the theorems). I lost hope that this already exist, but if somebody know some kind of software that comes very close, I would love to know! If nothing like this exist, I hope that I may be able to inspire some programmer here that such a game would be really awesome :)
Edit $\;$Would it be hard to program such a game ? I'm considering trying to program this myself. It feels like I only need to add some kind of campaign mode to GeoGebra. Or should I ask these question at stackoverflow?
Edit $\;$I was playng around a little bit with GeoGebra, but with these 3 constructions I cannot pass level 1 (constructing an equilateral triangle). I think I need to add another construction to the construction bar: Constructing a point at an intersection.