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Brunnian links are non-trivial links that cause a collection of links to collapse if cut. They can connect an infinite number of elements and have practical and theoretical applications in fields such as molecular biology. Brunnian links are often used in puzzles and symbolize strength in unity.
A Brunnian link is a non-trivial link in a collection of links that causes the entire collective to collapse if it is cut. A well-known example of Brunnian linkage are the Borromean rings, three rings that are connected in such a way that the removal of one ring would cause the whole to separate. Brunnian connections can potentially connect an infinite number of elements and are a topic of immense interest in knot theory, a branch of mathematics. While knot theory might not sound particularly brilliant, it’s actually a very interesting branch of the field of mathematics.
The Brunnian link is named after Hermann Brunn, a 19th-century mathematician who wrote about the phenomenon and covered it in an article. Besides being just interesting, Brunnian links can also have practical and theoretical applications. Molecular biologists, for example, have worked with Brunnian links to model various physical structures. Some people have also done a study on Brunnian braids, a closely related concept.
In things like Borromean rings, the individual links are knuckles, closed loops formed without knots. The most obvious example of an unknot is a simple loop, such as a ring, but unknots can also become extremely complex, and it is possible to create amazingly ornate structures of Brunnian links with unknots. The Brunnian connection illustrates the importance that a simple object or action can have, which is why Borromean rings are often used to symbolize strength in unity.
Three-dimensional modeling specialists have produced some very intriguing and complex working models of Brunnian links which easily illustrate the principle without the need for a physical example. Such templates are usually designed to allow users to manipulate them for several different angles, and you can remove a link to see an illustration of Brunnian’s link in action.
You may be more familiar with Brunnian links than you think. These links often play a vital role in puzzles that require their users to physically untangle different elements. When the user finds the correct method of manipulating the physical puzzle, they can make it fall apart and then the next challenge is to put it back together again. Puzzle rings are another well-known example of Brunnian linking, as most are designed so that if one ring is removed, the entire ring falls apart.
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