Tangloids

Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors.

A description of the game appeared in the book "Martin Gardner's New Mathematical Diversions from Scientific American" by Martin Gardner from 1996 in a section on the mathematics of braiding.

Two flat blocks of wood each pierced with three small holes are joined with three parallel strings. Each player holds one of the blocks of wood. The first player holds one block of wood still, while the other player rotates the other block of wood for two full revolutions. The plane of rotation is perpendicular to the strings when not tangled. The strings now overlap each other. Then the first player tries to untangle the strings without rotating either piece of wood. Only translations (moving the pieces without rotating) are allowed. Afterwards, the players reverse roles; whoever can untangle the strings fastest is the winner. Try it with only one revolution. The strings are of course overlapping again but they can not be untangled without rotating one of the two wooden blocks.

The Balinese cup trick, appearing in the Balinese candle dance, is a different illustration of the same mathematical idea. The anti-twister mechanism is a device intended to avoid such orientation entanglements. A mathematical interpretation of these ideas can be found in the article on quaternions and spatial rotation.