I’m a math nerd. I’ve actually never had any real professional math training. I just like studying mathematical concepts and figuring out formulas. In particular, I like any math that can be graphically visualized. If it can be animated, all the better. Computers and math and graphics and animation – that’s the stuff right there. If you’re in the UK, `:s/math/maths/g`

Recently I ran across an Android app called Euclidea. And soon discovered that while naturally there is an iOS app, there is also a web site that has all the same content.

Basically, there are 120 problems, or levels. In each level you need to construct some geometric form, place a point or line or form an angle that fulfills some criteria. The initial tools you have are a straight edge and a compass. As you figure out different techniques, those get added as shortcut tools. For example, using only a compass and a straight edge, you can form a line that bisects a given line segment. When you figure that out, you are given the perpendicular bisector tool that does that in a single step.

While simply solving a given level is OK, there are also goals to meet, such as solving it in a minimum number of steps. It gets a bit complex, but each problem has an L-score and an E-score. E is the number of Euclidean constructions. This would be a line drawn with the straight edge or a circle drawn with the compass. L is the number of “lines” drawn using any of the complex tools you discover. For example, using the perpendicular bisector tool would count as one L as you use that tool one time. But it counts as three Es, as it takes drawing two circles and a line.

Some of the problems – even on the higher levels – are fairly easy and straightforward. A few had me completely stumped and I had to resort to searching for an answer. Most of them I can solve, often within the L goal, but usually have a much harder time with the E goal. There’s even an active Quora community dedicated to the best solutions to the various problems. Fun stuff.

The Android app is free, but you have to solve a certain number of problems on lower levels with the correct L and E scores to unlock later levels. Or just pay to unlock everything. I paid.

[…] on Thales’ Theorem gave me an immediate realization on how I could solve a problem from Euclidea. Actually I had solved that problem, but had no clue how. Seeing and understanding Thales’ […]