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Android Games : Euclidea and Pythagorea (Do the Math!)


Let’s talk about educational games! That very phrase probably plunged you back into middle-school hell where you were compelled to play some janky math “game” on a crusty old school Windows box. That’s a shame, too. Educational games have a bum reputation, mainly because government contractors for public schools have a built-in audience whether they make a great game or a crappy game, so why put in any effort?


But over time, some great games have emerged from this underdog genre. Where in the World is Carmen Sandiego? is a beloved classic that spawned a whole franchise complete with a cartoon series. Then there’s The Oregon Trail, which may not inspire fond memories due to how tough it was, but has become a widespread meme anyway thanks to its universal deployment in the DOSBox ’90s.

But yes, sure, there were many clunkers in the “edutainment” genre of games too. Some of them, like Mario is Missing, we’ve even covered before in our list of worst moments in the Mario franchise. But we’re here instead to discuss the prospect of enjoyable edutainment. Not just any edutainment, no, but math at that!


Euclidea is a game about Pythagorean geometry

You can stop having an anxiety attack now. By “math” we mean the fun math, where you don’t have to do much actual calculation but proceed based on simple rules of geometry using nothing but points, lines, and circles. Euclidea is available for Google Play and Apple Store, free download with the option to pay to unlock all hints. It is a brilliantly designed, minimalist game with a tap-friendly interface that you’ll have no problem picking up.

Don’t worry about it if you slept through geometry class in high school, because this is your chance to catch up. Euclidea is more of a tutorial on Euclidean geometry itself, starting with the most basic premises of geometric theorems. You won’t have to do any adding or subtracting, but you will have to keep in mind abstract facts, for example that two intersecting circles of the same size can allow their intersection points to form the endpoints of a perpendicular line exactly half the distance between the center of the two circles. For that matter, you can find your way through most of the game without reading text, provided you’re keen on spatial reasoning.

Euclidea leads you along at a gentle learning curve, beginning with simple tasks and working their way up to more complex problems. Usually the solution will be either a dot or a shape in orange, which you must fit exactly. “Close enough” approximations don’t work here, so in several levels, you will have incorrect solutions which seem like they should get the same line or circle in the same place, but it’s just a hair off. Nope, that won’t do!

Your reward along the way is to unlock shortcut tools. You add to your set of compass and straightedge tools with an angle bisector, perpendicular bisector, and shortcuts for perpendicular and parallel lines. But to score in the game, you might have to find up to three solutions (some puzzles even a hidden fourth), including the most efficient and fewest moves. The shortcuts take their individual steps into account, so a tool to find the midpoint of a line automatically takes up a few moves. You can move on to the next level with any old solution, but only a near-“perfect” score will advance you to the next chapter of levels.

We’re really plumb out of features to talk about in Euclidea. There is no music, no flashy graphics, no dancing cartoon characters or daily bonus rounds. There are some intermediary flavor-text quotes from famous people in STEM history, that’s all. It’s a grown-up game for people who want to quietly ponder a puzzle.

Pythagorea and Pythagorea 60 – More of the same on grids

Horis International Unlimited, makers of Euclidea, continued in the same vein my moving along to the next logical mathematician: Pythagorea, named after Pythagoras. Likewise, Pythagorea is available for Google Play and Apple Store, free, with an optional in-game payment. This time we’re doing geometry on a grid, but otherwise our play is the same. You solve puzzles involving the construction of triangles, tangents, perpendiculars, and so on. If anything, Pythagorea is a lot less challenging and more elementary than Euclidea. Pythagorea 60 simply takes the same concept and moves you to a triangular, isometric grid.

Beyond that, the same company also has XSection, another geometry puzzle game. This time you’re solving problems in solid geometry, but be advised, it’s a freemium game where you have to pay to unlock all levels (or wait four hours per level to unlock!). XSection also has you solving a monotonous series of cross-section puzzles, a bit more advanced than our flat plane space where we started with Euclid back there.

Horis International, as you may have guessed by now, is on a crusade to make educational games both fun and instructive. The Euclid + Pythagoras series is definitely successful on that front; if you work anywhere in fields like engineering, CAD, graphic design, architecture, or anyplace else that applies geometry, these games will be a great refresher course and interesting exercise to stay sharp.

The Way Forward For Educational Games?

The problem with this genre is that not all STEM disciplines lend themselves to an elegant graphical representation which happens to make a fun game. A whole lot of educational games will play more like trivia, memorizing and answering quizzes. Even most math-based games struggle to come up with this much appeal.

But for what it’s worth, there are many more opportunities in recreational mathematics waiting to be discovered. An important potential guide to this field is Martin Gardner, the late Scientific American columnist who wrote a “Mathematical Games” feature for that publication and later collected his best columns into several books. He was the Willy Wonka of math teachers, and you have likely encountered one of his ideas or creations in various other puzzle game venues.

There is a website dedicated to preserving Gardner’s memory, which likely has the most complete listing of his mathematical game columns. Among the many topics he covered are principles which have been realized in toys and games both analog and digital, such as Nim, origami, mazes, and flexagons. But here again, these are specialized niches of mathematics, like topology and game theory, which lend themselves to games, but still comprise only a tiny corner of STEM pursuits.


In the same branch, Simon Tatham’s puzzle collection is a mini-game bundle, available free for all platforms including Android and Apple. They touch on several of the same subjects. The four-color map theorem is replicated exactly in one of Simon’s games.

While we’re talking about games, or at least recreational mathematics, founded by groundbreaking scientists, we should really discuss the greatest cellular automata ever made. It is perhaps provably the most perfect of its kind in the universe, invented by yet another renowned mathematician whom we sadly lost recently. But we’ll have to leave the amazing invention of John Conway for another time.

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