Morpion Solitaire is a very simple pencil-and-paper, line-drawing game for which the best possible score is not known! New records are still being set.
posted by Wolfdog on Jan 8, 2012 - 21 comments

The best known packings of equal circles within a circle. Best packings with 1-12 circles. Best packings with 49-60 circles. Best packings with 1093-1104 circles. Also, circles whose areas form a harmonic series. Circles in an isosceles right triangle. Or generate your own circle packings. (Background for beginners: circle packing. Background for experts: circle packing.)
posted by escabeche on Oct 19, 2011 - 29 comments

This short computer graphics animation presents the regular 120-cell: a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron. [more inside]
posted by Wolfdog on Aug 2, 2011 - 29 comments

Snowdecahedron. When life hands you a blizzard, make a Platonic solid. "Temporary public art" from Dan Sternof Beyer.
posted by escabeche on Feb 3, 2011 - 58 comments

Measure-theoretic probability: Why it should be learnt and how to get started. The clickable chart of distribution relationships. Just two of the interesting and informative probability resources I've learned about, along with countless other tidbits of information, from statistician John D. Cook's blog and his probability fact-of-the-day Twitter feed ProbFact. John also has daily tip and fact Twitter feeds for Windows keyboard shortcuts, regular expressions, TeX and LaTeX, algebra and number theory, topology and geometry, real and complex analysis, and beginning tomorrow, computer science and statistics.
posted by grouse on Dec 5, 2010 - 17 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

There's always been hyperbole in fashion; but fashion became truly hyperbolic this week when mathematican William Thurston, winner of a 1982 Fields Medal for his revolutionary re-envisioning of low-dimensional topology and geometry, teamed up with designer Dai Fujiwara (of the house of Issey Miyake) to produce a Paris runway show based on the fundamental geometries of 3-dimensional spaces. Thurston and Fujiwara briefly interviewed. Thurston's famous essay "Proof and Progress in Mathematics" concerns, among other things, Thurston's belief that the production of mathematical understanding can be carried out by means other than the writing down of formal proofs (though fashion shows are not specifically mentioned.) Previously in wearable non-Euclidean geometry: Daina Taimina's hyperbolic skirt.
posted by escabeche on Mar 8, 2010 - 19 comments

The eyeballing game: compare your best attempts at several instinctive everyday tasks - determining a point of convergence, bisecting an angle, finding the midpoint of a line - against mathematical certainty. In a more financial mood? Play Chartgame: given a random historical stock chart of an unnamed S&P 500 company, choose to buy and sell as time advances to see if you can beat the market.
posted by Bora Horza Gobuchul on Oct 14, 2009 - 22 comments

For math geeks. How to Draw the Voronoi Diagram. Voronoi diagrams, as a geometric model are fascinating because they can be used to describe almost literally everything: from cell phone networks to radiolaria, at every scale: from quantum foam to cosmic foam. See also the Wallpaper Group: there are only 17 ways to fill a plane with a regular 2 dimensional pattern. Fred Scharmen [weblog home] is known as 765 and also produces a number of shapes, textures and patterns.
posted by netbros on Sep 16, 2009 - 35 comments

A new crop circle formation in Wiltshire depicts the first 10 digits of pi. [more inside]
posted by casarkos on Jun 20, 2008 - 96 comments

The connection between mathematics and music is often touted in awed, mysterious tones, but it is grounded in hard-headed science. For example, mathematical principles underlie the organization of Western music into 12-note scales. And even a beginning piano student encounters geometry in the "circle of fifths" when learning the fundamentals of music theory. ...according to Dmitri Tymoczko, a composer and music theorist at Princeton University, these well-known connections reveal only a few threads of the hefty rope that binds music and math.

The Geometry of Music
See also The Geometry of Musical Chords - Dmitri Tymoczko, Science 7 July 2006: Abstract
See also Dmitri Tymoczko, Composer and Music Theoristvia [more inside]
posted by y2karl on Mar 16, 2008 - 29 comments

A Visual Dictionary of Famous Plane Curves is an outstanding resource for curves found in nature, man-made objects, and mathematics. Other websites that list exotically named curves also animate how they are created. One of the most unusually named curves, the “Witch of Agnesi”, has an unusual etymology. A number of these curves will be familiar to anyone who has used a Spirograph. Previously.
posted by Tube on Jan 19, 2008 - 13 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

Here are some beautifully rendered views of polytopes, and a few more. The rendering program, Jenn 3D, is free and downloadable, (OS X, Linux, Win) and includes some really dazzling fly-about and camera effects as well as tons of high-dimensional models to explore. There's also a mind-boggling possibility of playing Go on boards in projective space. Via the Math Paint blog, which leads to other interesting places...
posted by Wolfdog on Jun 2, 2007 - 13 comments

You have spacial skills. Apply them in Building Houses 2, on mathsnet.net. Or freestyle in Building Houses 1. Or at night! Oh and also there's like a hundred more puzzles over there too. Some java required.
posted by cortex on Apr 12, 2007 - 66 comments

Did the roof of the Pantheon influence Copernicus? Are the planets of the solar system aligned in accordance with a nearly-forgotten hypothesis known (unfairly) as Bode's Law? A fascinating wide-ranging discussion on BLDGBLOG with Walter Murch, the visionary editor and sound designer for such films as The Conversation, Apocalypse Now, The English Patient, THX1138, and many others. [Murch's film work has previously been discussed here and here.]
posted by digaman on Apr 7, 2007 - 20 comments

The Institute for Figuring presents the Crocheted Hyperbolic Coral Reef Project and Hyperbolic Crocheted Cacti and Kelp (more at this flickr gallery). If you secretly spend your evenings crocheting mathematical models, help build the coral reef or send a photo of your other creations to The People's Hyperbolic Gallery. (via Wonderland)
posted by madamjujujive on Sep 15, 2006 - 11 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

The Spidron is an interesting geometric construction that seems to lend itself to folding, dissection, and space-filling in two and three dimensions.
posted by Wolfdog on Jul 17, 2005 - 9 comments

The Geometry Center at the University of Minnesota, while now closed, maintains an awesome website with tons of math resources. I like sphere eversion, i.e. turning a sphere inside out. Link is to script of video, which explains things pretty well. Here is a clip [QT]. Also good: notes from a class on geometry and the imagination that John Conway and some friends gave awhile back. Old but good.
posted by mai on Mar 1, 2005 - 3 comments

The House With Too Many Perpundiculars
posted by DevilsAdvocate on Jul 13, 2004 - 8 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