Tuesday, March 5, 2013

'If Satan Plays Miniature Golf, This Is His Favorite Hole'

The headline above is the first sentence of a post on the Futility Closet blog describing a miniature golf hole. But there are no windmills, dinosaurs or clown's mouths on this mini-golf hole.

Instead, this is a simple schematic of a 24-sided mini-golf green that looks like this:



In the drawing above, "B" represents the hole. "A" is the aiming point. Stand anywhere you want on this green and strike the ball as hard as you want at point A. Assume the golf ball will continue bouncing for as along as it takes to eventually find the Hole B.

Guess what? The ball will never go into Hole B. The golf ball can bounce around this putting green forever and will never go into Hole B.

Well, sure, you could just aim at Hole B rather than striking your putt toward Point A. But this is actually a mathematical puzzle, not an example of real-world putt-putt golf.

Futility Closet explains the origin of the configuration in the schematic above:
"The idea arose in the 1950s, when Ernst Straus wondered whether a room lined with mirrors would always be illuminated completely by a single match."
In other words, if every wall is a mirror, can you design a room so that there will be a "dark spot," a spot at which you can stand without being able to see any light from a match's flame even though the walls are mirrors. The answer, it turns out, is yes. If the light source is Point A, its light will bounce around those mirrored walls without ever being visible to a person standing at Point B.

OK, maybe a post about a clown's mouth would have been more exciting. Hey, nobody warned me there was going to me math!

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