Borromean Rings

depicted in crop circle at Alton Barnes, Wiltshire
from 4th may 2008

By Glenn Aoys Netherlands

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Updated Monday 12th  May 2008

 


As always I use my sixth sense and mathematics to guide me in the meaning of the symbols in crop circles and so I get to the following conclusion.


 

Watch the small black dot, left picture. That’s the view point and so it resembles the right picture exactly. The circle in the middle is added by the unknown formation makers.  It could be that they mean the Earth and that they use this symbol to explain that Earth will last forever, whatever will happen!

 There is a lot to find about the Borromean Rings at Wikipedia, there is even a site devoted to the rings, http://www.liv.ac.uk/~spmr02/rings/index.html

 

Extracted from Wikipedia
In mathematics, the Borromean Rings consist of three topological circles which are linked and form a Brunnian link, i.e., removing any ring results in two unlinked rings.

Mathematical properties

Although the typical picture of the Borromean rings (left picture) 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 (centre picture).

http://upload.wikimedia.org/wikipedia/commons/thumb/c/c2/BorromeanRings.svg/120px-BorromeanRings.svg.png

Standard diagram of the Borromean rings

http://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/MolecularBorromeanRing.jpg/120px-MolecularBorromeanRing.jpg

A realization of the Borromean rings as ellipses

http://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Hallsberg_vapen.svg/99px-Hallsberg_vapen.svg.png

Coat of arms showing padlocks locked in Borromean rings configuration

The Borromean rings give examples of several interesting phenomena in mathematics. One is that the cohomology of the complement supports a non-trivial Massey product. Another is that it is a hyperbolic link: the complement of the Borromean rings in the 3-sphere admits a complete hyperbolic metric of finite volume. The canonical (Epstein-Penner) polyhedral decomposition of the complement consists of two ideal octahedra.

History of origin and depictions

The Borromean rings as a symbol of the Christian Trinity, from a 13th-century manuscript.

http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png

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.

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.

A monkey's fist knot is essentially a 3-dimensional representation of the Borromean rings, albeit with 3 layers, in most cases.

It should also be noted that the Borromean rings appear in Ghandarva (Afghan) Buddhist art from around the second century C.E.

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.


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