Ancient Greek philosophers once speculated that it was possible to draw any geometric shape using only a compass and a ruler. We now know that's not true, but you'd be surprised just how much you can achieve using these simple tools. If you have a couple of hours to spare (trust me, you'll get sucked in to this), you can demonstrate this for yourself by playing Euclid the Game.
The early levels are pretty easy, but soon enough you'll be using multiple steps to draw the circumcircle around a triangle:
The really cool thing about the game is that as you solve simpler problems — say, how to bisect an angle — the solution becomes a new tool you can use in later problems. In other words, theorems become icons. Genius! You do get a bonus for solving the problems with just the basic ruler and straight-edge, but I love the way your toolset builds up as you go. Even if you hated geometry class at school, give it a try: you might enjoy Euclid the Game as much as I did.
That's all for the (big!) week for us! (You can check out out previous Friday posts here.) See you back here on Monday for a new week of blogging.
I'd recommend linking to http://en.wikipedia.org/wiki/Constructible_polygon rather than squaring the circle in the context of what can be constructed.
Posted by: Edward | January 23, 2015 at 14:00