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In mathematics, the Borromean rings consist of three topological circles which are linked despite the fact that no two of them are linked, i.e. they form a Brunnian link. Although the typical picture of the Borromean rings (see right) may lead one to think the link can be formed from geometrically round circles, the Brunnian property means they cannot (see "References"). It is, however, true that one can use ellipses of arbitrarily small eccentricity (see picture below).
History of origin and depictions
The name "Borromean rings" comes from their use in the coat of arms of the aristocratic Borromeo family in Italy. The link itself is much older and has appeared in the form of the valknut on Norse image stones dating back to the 7th century.
The Borromean rings have been used in different contexts to indicate strength in unity, e.g. in religion or art. In particular, some have used the design to symbolize the Trinity. The psychoanalyst Jacques Lacan famously found inspiration in the Borromean rings as a model for his topology of the human mind, with each ring representing a fundamental Lacanian component of reality (the "real", the "imaginary", and the "symbolic").
The Borromean rings were also the logo of Ballantine beer.
Partial Borromean rings emblems
In medieval and renaissance Europe, a number of visual signs are found which consist of three elements which are interlaced together in the same way that the Borromean rings are shown interlaced (in their conventional two-dimensional depiction), but the individual elements are not closed loops. Examples of such symbols are the Snoldelev stone horns and the Diana of Poitiers crescents.
Knots as Borromean rings
The three coils of cordage in a Monkey's fist form in effect a set of Borromean rings in three dimensions.
Molecular Borromean rings
In 1997, biologists Chengde Mao and coworkers of New York University succeeded in constructing Borromean rings from DNA (Nature, vol 386, page 137, March 1997).
In 2003, chemist Fraser Stoddart and coworkers at UCLA utilised coordination chemistry to construct molecular Borromean rings in one step from 18 components. This work was published in Science 2004, 304, 1308-1312. Abstract
See also
References
- B. Lindström, "Borromean Circles are Impossible", American Mathematical Monthly, volume 98 (1991), pages 340—341. This article explains why Borromean links cannot be exactly circular.
External links
- Site devoted to the Borromean Rings.
- The Borromean link and related entities in knot theory
- The Borromean Rings at the wiki Knot Atlas.
- History of the Borromean rings
"Borromean rings"