Sunday, August 23, 2015

The Game of Loop

Alex Bellos designed and commissioned a pool table that is an ellipse. This has been up on Numberphile for about a month, but I saw it again on BBC just now. Along with this, he has devised a rather fun game that he talks about in the video as well as on BBC here.

An ellipse is a geometric shape that is commonly referred to as a conic section. Other examples of conic sections are parabolas and circles. The geometric definition of an ellipse is "the locus of all points", (that is all of the possible points) such that the sum of the distances to the two focal points is constant for every point on the curve. Interestingly, a circle is just a special kind of ellipse where the two foci are at the same point.

The really cool part of this is that if you were to draw a line to the edge of an ellipse from either focus, the reflection would draw a line through the other focus. For the game above, this is the core. That means that a player must be cognizant of the other focus of the ellipse in order to sink the ball into the hole, which sit on the other focus. Watch the videos, and enjoy the gameplay. I, for one, want one of these tables...

I'm working on another write up that will talk about ellipses, hopefully to post later this week. My buddy Tyler asked me about how we solved for the distance between the Earth and the Sun, using a pair of Venus transits across the Sun. I'll post that soon!