Connection With Braids
If one cuts the Borromean rings, one obtains one iteration of the standard braid; conversely, if one ties together the ends of (one iteration of) a standard braid, one obtains the Borromean rings. Just as removing one Borromean ring unlinks the remaining two, removing one strand of the standard braid unbraids the other two: they are the basic Brunnian link and Brunnian braid, respectively.
In the standard link diagram, the Borromean rings are ordered non-transitively, in a cyclic order. Using the colors above, these are red over yellow, yellow over blue, blue over red – and thus after removing any one ring, for the remaining two, one is above the other and they can be unlinked. Similarly, in the standard braid, each strand is above one of the others and below the other.
Read more about this topic: Borromean Rings
Famous quotes containing the words connection with and/or connection:
“We live in a world of things, and our only connection with them is that we know how to manipulate or to consume them.”
—Erich Fromm (1900–1980)
“The virtue of art lies in detachment, in sequestering one object from the embarrassing variety. Until one thing comes out from the connection of things, there can be enjoyment, contemplation, but no thought.”
—Ralph Waldo Emerson (1803–1882)