Borromean rings: Encyclopedia - Borromean rings

Borromean rings

In mathematics, the Borromean rings consist of three topological circles which are linked despite the fact that no two of them are linked (they form a Brunnian link). This link cannot be formed from actual geometrically round circles, although you can use ellipses of arbitrarily small eccentricity.

Borromean rings - 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").

Borromean rings - 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

• link (mathematics)
• knot theory

Adapted from the Wikipedia article "Borromean rings", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki