16 posts tagged with Mathematics *and* geometry. (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

Paper Matrix is a blog that gives instructions for cool papercraft objects, "reinterpreting the Danish tradition of woven paper hearts and ornaments." Cut paper in the prescribed ways and weave it together carefully to make a mobile of colorful hot air balloons, gorgeous and complex boxes; simple but satisfying pennants and much more... including a full theater for performances by paper dolls.

posted by LobsterMitten on Sep 23, 2013 - 18 comments

posted by LobsterMitten on Sep 23, 2013 - 18 comments

The regular polygons have been kidnapped by ninjas. Are you a bad enough dude/tte to construct the regular polygons with nothing but a virtual compass and straightedge? [more inside]

posted by Iridic on Jul 3, 2013 - 67 comments

posted by Iridic on Jul 3, 2013 - 67 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

"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

Henry Segerman creates mathematical sculptures using 3D printing:
Round Möbius Strip,
Hopf Fibration,
Half of a 120-cell,
Rectified Tesseract,
Tesseract and 16-cell,
Hilbert Curve,
Knotted Cogs,
Round Klein Bottle [more inside]

posted by Foci for Analysis on Sep 10, 2011 - 12 comments

posted by Foci for Analysis on Sep 10, 2011 - 12 comments

Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]

posted by ErWenn on Dec 3, 2010 - 27 comments

Mathematicians create videos that help in visualizing four-dimensional objects. Science News writes about it: seeing in four dimensions.

posted by Surfin' Bird on Aug 24, 2008 - 26 comments

posted by Surfin' Bird on Aug 24, 2008 - 26 comments

Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)

posted by parudox on Dec 1, 2007 - 11 comments

posted by parudox on Dec 1, 2007 - 11 comments

The Johnson Solids are a set of 92 semi-regular polyhedra, all of which are uniquely named and numbered. Except for the familiar square pyramid they all have exotic names like the Hebesphenomegacorona. A Hebesphenomegacorona in space. Number 26, the Gyrobifastigium, is unique in that if copies of itself are properly stacked together they will leave no gaps, thus making it the only space filling Johnson Solid.

posted by Tube on Oct 3, 2007 - 28 comments

posted by Tube on Oct 3, 2007 - 28 comments

What if Euclid had been Japanese? There are traditionally stated and proved theorems *about* origami. And MetaFilter has previously explored modular origami (as well as the boring old artistic kind), which has a geometric foundation. However, origami itself is a powerful mathematical framework that allows one to, for instance, solve the famously insoluable problem of trisecting an angle. More generally: Traditional geometry solves quadratic equations, origami solves cubic ones. (Many more mathematical items about and using origami can be found in the excellent mathematics teachers' book: Project Origami: Activities for Exploring Mathematics, most of which are unfortunately not findable online).

posted by DU on Feb 13, 2007 - 9 comments

posted by DU on Feb 13, 2007 - 9 comments

Jim Loy's Mathematics Page is (among other things) a collection of interesting theorems (like Napoleon's Triangle theorem), thoughtful discussions of both simple and complex math, and geometric constructions (my personal favorite); the latter of which contains surprisingly-complex discussions on the trisection of angles, or the drawing of regular pentagons.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

posted by odinsdream on Sep 14, 2005 - 8 comments

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

posted by odinsdream on Sep 14, 2005 - 8 comments

Astonishing geometric art using only folded paper plates, from Bradford Hansen-Smith at wholemovement. View the gallery of fantastic polyhedral creations, and learn how to do it yourself. (For more fun with paper plates, see also Paper Plate Education: Serving the Universe on a Paper Plate.)

posted by taz on Oct 27, 2003 - 7 comments

posted by taz on Oct 27, 2003 - 7 comments

'The Poincare Conjecture' Solved? "Dr Grigori Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences, St Petersburg, claims to have proved the Poincare Conjecture, one of the most famous problems in mathematics. The Poincare Conjecture, an idea about three-dimensional objects, has haunted mathematicians for nearly a century. If it has been solved, the consequences will reverberate throughout geometry and physics."

Also of note is that Perelman's solution is only a benign side effect of his efforts toward defining all three-dimensional surfaces mathematically, which if successful would allow humanity to "produce a catalogue of all possible three-dimensional shapes in the Universe, meaning that [mankind] could ultimately describe the actual shape of the cosmos itself."

posted by eyebeam on May 8, 2003 - 13 comments

Also of note is that Perelman's solution is only a benign side effect of his efforts toward defining all three-dimensional surfaces mathematically, which if successful would allow humanity to "produce a catalogue of all possible three-dimensional shapes in the Universe, meaning that [mankind] could ultimately describe the actual shape of the cosmos itself."

posted by eyebeam on May 8, 2003 - 13 comments

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