 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). Image File history File links borromean rings / knot, painted by User:Kku in Gimp, 2. ...
Euclid, detail from The School of Athens by Raphael. ...
A circle, in Euclidean geometry, is the set of all points at a fixed distance, called the radius, from a fixed point, the centre. ...
The Borromean rings, a link with three components each equivalent to the unknot. ...
In mathematics, a Brunnian link is a nontrivial link that become trivial if any number of components are removed. ...
(This page refers to eccentricity in mathematics. ...
History of origin and depictions
 The Borromean rings as a symbol of the Christian Trinity, from a 13th-century manuscript. 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. Image File history File links BorromeanRings-Trinity. ...
Image File history File links BorromeanRings-Trinity. ...
For other uses, see Trinity (disambiguation). ...
A modern coat of arms is derived from the medi val practice of painting designs onto the shield and outer clothing of knights to enable them to be identified in battle, and later in tournaments. ...
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Odin with Sleipnir, Valknuts are drawn beneath the horse (Tängelgarda stone) The valknut (Old Norse valr, slain warriors + knut, knot) is a symbol consisting of three interlocked triangles. ...
Norsemen (the Norse) is the indigenous or ancient name for the people of Scandinavia, including (but not limited to) the Vikings. ...
A rune stone Rune stones are somewhat flat standing stones with runic stone carvings from the Iron Age (Viking Age) and early middle ages found in most parts of Scandinavia. ...
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"). For other uses, see Trinity (disambiguation). ...
Cover of Elisabeth Roudinescos biography of Lacan Jacques-Marie-Émile Lacan (April 13, 1901 – September 9, 1981) was a French psychoanalyst and psychiatrist. ...
The Borromean rings were also the logo of Ballantine beer. Ballantine was an American brewery, founded by Peter Ballantine who was born in Scotland in 1781. ...
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. The Viking Age (Younger Futhark) runestone at Snoldelev, Ramsø, Denmark, dated to ca. ...
Diane de Poitiers (September 3, 1499 - April 25, 1566) was a fixture at the courts of several French kings, and became notorious as the mistress of King Henri II. She was born in the château de Saint-Vallier, in the town of Saint-Vallier, Drôme, in the Rh...
Molecular 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). Image File history File links MolecularBorromeanRing. ...
Image File history File links MolecularBorromeanRing. ...
1997 (MCMXCVII in Roman) is a common year starting on Wednesday of the Gregorian calendar. ...
Biology is a branch of science, dealing with the study of life. ...
New York University (NYU) is a major research university in New York City. ...
The general structure of a section of DNA Deoxyribonucleic acid (DNA) is a nucleic acid —usually in the form of a double helix— that contains the genetic instructions specifying the biological development of all cellular forms of life, and most viruses. ...
First title page, November 4, 1869 Nature is one of the oldest and most reputable scientific journals, first published on 4 November 1869. ...
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 2003 (MMIII) was a common year starting on Wednesday of the Gregorian calendar. ...
Multicolored chemicals are frequent hallmarks of chemistry. ...
James Fraser Stoddart is a British chemist at the Department of Chemistry and Biochemistry University of California, Los Angeles. ...
The University of California, Los Angeles, popularly known as UCLA, is a public, coeducational university situated in the neighborhood of Westwood within the city of Los Angeles. ...
complex In chemistry, a complex is a structure composed of a central metal atom or ion, generally a cation, surrounded by a number of negatively charged ions or neutral molecules possessing lone pairs. ...
Topology of a Borromean ring Molecular Borromean rings are the molecular pendants of Borromean rings and a kind of catenane. ...
Science is the journal of the American Association for the Advancement of Science (AAAS). ...
See also The Borromean rings, a link with three components each equivalent to the unknot. ...
Trefoil knot, the simplest non-trivial knot. ...
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.
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