Borromean Rings

The Borromean rings are a set of three topological circles that are linked together such that removing any one of the three rings frees the other two, even though no two of the rings are linked with each other on their own, a property called a Brunnian link. The rings take their name from the Italian House of Borromeo, which used the symbol in its coat of arms, although the same figure appears far earlier in the history of many cultures, including as a Norse symbol called the valknut and in Christian iconography representing the Holy Trinity. While the rings are traditionally drawn as geometrically circular, no configuration of three true geometric circles can form the Borromean rings, so a mathematically faithful realization requires the rings to be at least slightly non circular; the figure is nonetheless of genuine interest in knot theory as the simplest example of a Brunnian link with three components.