The Borromean rings, also called the Borromean links (Livingston 1993, p. 10), are three mutually interlocked rings, illustrated schematically above and named after the Italian Renaissance family who used them on their coat of arms. The configuration of rings is also known as a "Ballantine." In the Borromean rings, no two rings are linked, so if any one of the rings is cut, all three rings fall apart. Any number of rings can be linked in an analogous manner (Steinhaus 1999, Wells 1991).
Ballantine's Ale, brewed by the Falstaff Brewing Corporation, used the three-ring motif on the beer coaster illustrated above.
It turns out that rigid Borromean rings composed of real (finite thickness) tubes cannot be physically constructed using three circular rings of either equal or differing
radii. However, they can be made from three congruent elliptical rings.
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and are also the simplest Brunnian link.
