A faster Web from group theory? A February 8 New York Times article (John Markoff) tells about network design hotshot Alan Huang who applies group theory to the problem of routing internet traffic. He calls his patented design a Galois network "in a tip of the hat to the French pioneer of group theory."
Unknots that can't be untied: a note in the February 12 Science describes Jason Cantarella and Heather Johnston's discovery of chains of rigid segments which are topologically unknotted but geometrically undisentangleable. Here is one of their unknots (image used with permission):
For full details see their paper Nontrivial Embeddings of Polygonal Intervals and Unknots in 3-space, to appear in J. Knot Theory Ramifications.
where g = 1.618033... is the ``golden section.'' The picture just shows that part of the surface within 2.1 units of the origin in (x, y, z)-space. The images are by Paolo Dominici (email@example.com) of Todi, Italy, and are here used with permission. Dominici has also posted a fly-through of this surface.
Comments: Email Webmaster