Mathematical Properties
Although the typical picture of the Borromean rings (above right picture) may lead one to think the link can be formed from geometrically round circles, they cannot be. (Freedman & Skora 1987) proves that a certain class of links, including the Borromean links, cannot be exactly circular. Alternatively, this can be seen from considering the link diagram: if one assumes that circles 1 and 2 touch at their two crossing points, then they either lie in a plane or a sphere. In either case, the third circle must pass through this plane or sphere four times, without lying in it, which is impossible; see (Lindström & Zetterström 1991).
It is, however, true that one can use ellipses (right picture). These may be taken to be of arbitrarily small eccentricity; i.e. no matter how close to being circular their shape may be, as long as they are not perfectly circular, they can form Borromean links if suitably positioned: for example, Borromean rings made from thin circles of elastic metal wire will bend.
Read more about this topic: Borromean Rings
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