Borromean Rings

Borromean rings are said to have originated from Afghan Buddhist art in the 2nd century, but realistically they could date back to earlier civilisations.Borromean rings #

In 15th century Italy, the Borromeo family’s crest included this pattern of three intertwining rings; the rings were “depicted in such a way so that if one of the rings were cut, all three would separate, implying greater strength through unity“. This feature is called a Brunnian link, i.e. removing any ring results in two unlinked rings.

Coat of arms of the House of Borromeo.svg

Coat of Arms of the House of Borromeo | Source: Wikipedia

These rings have been discovered to occur at a molecular level in DNA and in other nanotechnology research, where they are linked in 3-dimensions rather than on a flat plane.

 

File:Molecular Borromean Rings Atwood Stoddart commons.jpg

Molecular Borromean Rings | Source: Wikipedia

Although the typical picture of Borromean rings leads us to believe that this link can be formed from geometrically ideal circles, or in other words constructed using three circular rings of either equal or differing radii, in fact it turns out that this cannot be. However, they can be made from three congruent elliptical rings, whose eccentricity may be taken to be arbitrarily small, i.e. “no matter how close to being circular their shape may be, as long as they are not perfectly circular“.

Borromean Rings as ellipses

Update: I think I’m going to change my schedule to Monday and Thursday! I think 2 posts a week is more manageable due to my new university schedule…

M x

 

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