Saturday, June 29, 2019
Borromean Rings
The Borromean rings, also called the Borromean links are three mutually
interlocked rings, named after the Italian Renaissance family who used them on
their coat of arms. The configuration of rings is also known as a “Ballantine,”
and a brand of beer has been brewed under this name. 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).
The Borromean rings are a prime link. They
have link symbol
06-0302, braid word ,
and are also the simplest Brunnian link.
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.
Friday, June 28, 2019
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