Follow

en.wikipedia.org/wiki/Borromea is now a Good Article on Wikipedia. You can't make the Borromean rings with geometric circles: as Tverberg observed, an inversion would make one of them a line. But then each of the other two circles would span an angle less than π as viewed from the line, leaving an unspanned direction along which the line could escape to infinity, contradicting the inseparability of the rings.

· · Web · 1 · 1 · 3

Same proof works for four pairwise-unlinked circles: move them until two circles touch, and invert at the touching point to get two parallel lines and two circles. The two circles each block a range of directions less than π and the other line only blocks a single direction, so each line still has a direction along which it can escape to infinity, separating the two lines from the two circles.

Sign in to participate in the conversation
Mathstodon

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!