14 posts tagged with Mathematics *and* topology. (View popular tags)

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Trio for Three Angles (1968) is one of many beautiful acclaimed visually-oriented short films with music by mathematical filmmakers Bruce and Katharine Cornwell, some animated by hand and some using early digital technology. It inspired three sequels: Similar Triangles (1975), Congruent Triangles (1976), and Journey to the Center of a Triangle (1978) (previously). [more inside]

posted by beryllium on Jul 6, 2014 - 5 comments

posted by beryllium on Jul 6, 2014 - 5 comments

Mathematicians Henry Segerman and Saul Schleimer have produced a triple gear, three linked gears in space that can rotate together. A short writeup of the topology and geometry behind the triple gear on the arXiv.

posted by escabeche on Apr 26, 2013 - 36 comments

posted by escabeche on Apr 26, 2013 - 36 comments

Robert MacPherson interviewed as part of the Simons Foundation's Science Lives series. MacPherson is among the founders of the modern theory of *singularities*, points like a kink in a curve where the geometry of a space stops being smooth and starts behaving badly. In the interview, MacPherson talks about cultural differences between math and music, his frustration with high school math, growing up gay in the South and life as a gay man in the scientific community, smuggling $23,000 in cash into post-Soviet Russia to help mathematicians there keep the lights on, catastrophe theory, perverse sheaves, how to be a successful graduate student, stuttering, and of course the development of the intersection homology theory for which he is most well-known.

posted by escabeche on Sep 12, 2012 - 5 comments

posted by escabeche on Sep 12, 2012 - 5 comments

The fine people over at the International Guild of Knot Tyers Forum talk knots. On Mars.

posted by Foci for Analysis on Sep 4, 2012 - 33 comments

posted by Foci for Analysis on Sep 4, 2012 - 33 comments

"The real satisfaction from mathematics is in learning from others and sharing with others." William Thurston, one of the greatest mathematicians of the 20th century, has died. He revolutionized topology and geometry, insisting always that geometric intuition and understanding played just as important a role in mathematical discovery as did the austere formalism championed by the school of Grothendieck. Thurston's views on the relation between mathematical understanding and formal proof are summed up in his essay "On Proof and Progress in Mathematics." [more inside]

posted by escabeche on Aug 22, 2012 - 32 comments

posted by escabeche on Aug 22, 2012 - 32 comments

Science through yarn: Wooly Thoughts. The Home of Mathematical Knitting, including knitted klein bottles and hyperbolic planes. The Museum of Scientifically Accurate Fabric Brain Art (previously). Much, much, more on knitting, crochet and quilting used to visualize complex theories in topology, probability, chaos and fractals. [more inside]

posted by Bora Horza Gobuchul on Nov 6, 2011 - 8 comments

posted by Bora Horza Gobuchul on Nov 6, 2011 - 8 comments

So you're me and you're in math class and you're learning about graph theory, a subject too interesting to be included in most grade school's curricula so maybe you're in some special program or maybe you're in college and were somehow not scarred for life by your grade school math teachers. [more inside]

posted by achmorrison on Feb 22, 2011 - 32 comments

posted by achmorrison on Feb 22, 2011 - 32 comments

"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

posted by escabeche on Apr 23, 2009 - 30 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

posted by Blazecock Pileon on Jun 27, 2008 - 22 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

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

posted by Gyan on Aug 29, 2006 - 17 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

posted by kliuless on Aug 15, 2006 - 32 comments

The Shapes of Space [note : *pdf, sciam, poincaré conjecture*]

posted by kliuless on Aug 1, 2004 - 4 comments

posted by kliuless on Aug 1, 2004 - 4 comments

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