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Borromean rings
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). In other words, no two of the three rings are linked with each other as a Hopf link, but nonetheless all three are linked.
== 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 ideal circles, they ''cannot be''. Freedman and Skora (1987) prove 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 .
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; as an example, thin circles made from bendable elastic wire may be used as Borromean rings.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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