Geometric vanishing puzzles use principles of mathematics to create a magical optical illusion. The most famous one, Get off the Earth, sold over ten million copies, and was created in 1898 by Sam Lloyd. He was an American puzzle maker, mathematician, chess player and occasional conman who sometimes took credit for other toys which he hadn't actually invented.
The puzzle portrays thirteen Chinese warriors around the rim of circular pieces of cardboard which are attached in such a way as to form a rotatable dial. By rotating the outer ring, one of the warriors mysteriously drops out of sight; the challenge is to work out how this has happened. The solution to the puzzle has a mathematical explanation based on what is known as 'the principle of concealed distribution'. The warriors are arranged so that, by turning the ring, a small portion of one warrior is added to each of the other warriors, they become fractionally bigger and one of them apparently vanishes!
The principle behind this now-classic puzzle can easily be demonstrated by drawing ten parallel and equidistant lines on a piece of paper. The two outer lines need to meet with a diagonal dotted line on the paper. Once the paper is cut in half along the
dotted line the lower piece can be angled so that one of the lines cannot be seen. As in the warrior puzzle the remaining lines have become slightly
longer because they have each taken a small slice of the vanishing line. Many such variations of this vanishing puzzle have been catalogued; all showing maths can be magic.