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March 1999
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." Virtual rapids, fingerless flows and tournament seedings are featured as "vividly realworld applications" of mathematics in Science's February 12 survey of the AMS San Antonio meetings. 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 3space, to appear in J. Knot Theory Ramifications.
This symmetric singular sextic surface appears on the cover of the March, 1999 AMS Notices. The equation is 4(g^{2}x^{2}y^{2})(g^{2}y^{2}z^{2})(g^{2}z^{2}x^{2})(1+2g)(x^{2}+y^{2}+z^{2}1)^{2}=0, 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 (pd@fullservice.it) of Todi, Italy, and are here used with permission. Dominici has also posted a flythrough of this surface. Tony Phillips

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