"the scale-free network modeing paradigm is largely inconsistent with the engineered nature of the Internet..." For a decade it's been conventional wisdom that the Internet has a scale-free topology, in which the number of links emanating from a site obeys a power law. In other words, the Internet has a long tail; compared with a completely random network, its structure is dominated by a few very highly connected nodes, while the rest of the web consists of a gigantic list of sites attached to hardly anything. Among its other effects, this makes the web highly vulnerable to epidemics. The power law on the internet has inspired a vast array of research by computer scientists, mathematicians, and engineers. According to an article in this month's Notices of the American Math Society, it's all wrong. How could so many scientists make this kind of mistake? Statistician Cosma Shalizi explains how people see power laws when they aren't there: "Abusing linear regression makes the baby Gauss cry."
posted by escabeche on Apr 23, 2009 - 30 comments

Topology and Geometry Software by Jeff Weeks.
posted by Eideteker on Apr 22, 2009 - 5 comments

Whether you want to learn to lace shoes, tie shoelaces, stop shoelaces from coming undone, calculate shoelace lengths or even repair aglets, Ian's Shoelace Site has the answer!
posted by Blazecock Pileon on Jun 27, 2008 - 22 comments

Inside Out A topographical bedtime story. (Warning, contains spheres!)
posted by loquacious on Aug 28, 2007 - 20 comments

Can you cut a hole in a 3x5 card that's large enough to crawl through? Topological trickery and some other classic science experiments.
posted by Wolfdog on Jul 2, 2007 - 40 comments

Dr. Jeannine Mosely finishes building a level-3 Menger sponge from business cards. You can also build your own, though Dr. Mosely warns, "[a] level 4 sponge would require almost a million cards and weigh over a ton. I do not believe it could support its own weight — so a level 3 is the biggest sponge we can hope to build." (related)
posted by Blazecock Pileon on Feb 2, 2007 - 19 comments

Grigory Perelman, awarded the Fields Medal for his work on the Poincare Conjecture, talks to the New Yorker.
posted by Gyan on Aug 29, 2006 - 17 comments

Bending a soccer ball - mathematically. Found via Ivars Peterson's short exposition on Braungardt and Kotschick's The Classification of Football Patterns [pdf, technical].
posted by Wolfdog on Aug 17, 2006 - 18 comments

Grisha Perelman, where are you? Perelman has quite possibly solved one of mathematics biggest mysteries, Poincaré’s conjecture, but has since disappeared.
posted by kliuless on Aug 15, 2006 - 32 comments

Pretty and pretty interesting: unrooted haplotype networks -- diagrams showing the relation and mutational distance between different sets of DNA, with haplotypes represented by circles proportional to haplotype frequency, joined by lines proportional to mutational difference between haplotypes -- in cichlid fish (on page 3 ) [pdf], in stone loach fish ( on page 3) [pdf], in lesser prairie chickens (on page 6) [pdf] and in a ring species! (on page 2) [pdf]
posted by orthogonality on Mar 25, 2005 - 14 comments

Beautiful Mathematical Surfaces : "Conceptual Forms," a series of photographs by Hiroshi Sugimoto, conceived as an hommage to Marcel Duchamp (English summary) and as an un-Man Ray-like treatment of the subject, consisting of (English summary) "Mathematical Forms" ("Curves" and "Surfaces") and Mechanical Forms.
posted by Zurishaddai on Dec 12, 2004 - 10 comments

The Shapes of Space [note : pdf, sciam, poincaré conjecture]
posted by kliuless on Aug 1, 2004 - 4 comments

After getting the inside story (ha?) on the inventor of everyone's favorite non-orientable surface, the Klein Bottle; and perhaps playing a few games inside of one, you can check out a few 3-dimensional immersions of klein bottles: in Lego, knitted fabric, paper, or glass.
posted by kidsplateusa on Oct 30, 2000 - 5 comments