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What's New in Mathematics 0399 *March 1999*

Snow Sculpting with Mathematics A faster Web from group theory? Real-world applications Unknots that can't be untied Symmetric singular sextic surface

Snow Sculpting with Mathematics A 12-foot high Costa surface made of snow was entered at the 9th annual Breckenridge (Colo.) International Snow Sculpture Championships this year. The sculpture, entitled *Invisible Handshake*, was carved by a team from Macalester College, directed by mathematical sculptor Helaman Ferguson, and sponsored by Wolfram Research, Inc. For more information on the Costa surface, see pages by Eric Weisstein, Sam Ferguson, and the GRAPE project at Bonn. | **Stan Wagon and Helaman Ferguson putting the final touches on** the Costa surface. Photo by Dan Schwalbe, used with permission. |

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 real-world 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 3-space*, 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+2*g*)(*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@full-service.it) of Todi, Italy, and are here used with permission. Dominici has also posted a fly-through of this surface.

* -Tony Phillips*

SUNY at Stony Brook

Math in the Media Archive