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

Pattern in Islamic Art - thousands of high quality, free pictures of various motifs, patterns and architectural elements of mosques and other structures from Asia to West Africa. [more inside]
posted by Burhanistan on Aug 6, 2009 - 31 comments

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

Jared Tarbell is a computer artist whose Gallery of Computation has been previously featured on Metafilter . Several years ago he began working with the Epilog Mini 24 laser cutter, cutting out flat cardboard pieces and assembling them into complex geometric shapes. His Flickr set “lased” documents his work. Recently he made the transition to a more traditional artistic medium; oiled walnut , for his stunning piece 2222 holes.
posted by Tube on Feb 19, 2009 - 23 comments

Structure Synth is an application for creating 3D structures from a set of user specified rules. It is an attempt to make a 3D version of Context Free.
posted by signal on Jan 2, 2009 - 8 comments

Curtis Steiner is a Seattle businessman and artist who operates a local gift shop. Both his home and his shop have garnered positive press, but his greatest artistic achievement may be his piece entitled 1,000 blocks, which explores the permutations of the six facets of the cube.
posted by Tube on Dec 21, 2008 - 30 comments

Dave Bollinger is a computer artist that specializes in geometry. He creates both still images and short videos. Some videos are silent, like this unusual Pac-Man homage, and some have soundtracks. Some are in black and white and some are in color. His Flickr photostream categorizes still images by style. His current fascination seems to be with cubes and cubic lattices.
posted by Tube on Nov 27, 2008 - 5 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

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

Polyhedral Maps is a website that explores unconventional methods of mapping the surface of the earth. The most famous of these unusual maps was Buckminster Fuller’s Dymaxion map, which used the net of an icosahedron. Da Vinci had experimented with this technique in his “Octant” map of 1514, which used Reuleaux triangles as map elements. This process is now being used by photographers and artists in manipulating panoramic images. A good example is Tom Lechner’s The Wild Highways of the Elongated Pentagonal Orthobicupola.
posted by Tube on Jun 1, 2008 - 23 comments

It's art; it's geometry; it's green tech. It's the oloid. [more inside]
posted by No Robots on Mar 18, 2008 - 20 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

Vladimir Bulatov enjoys making polyhedra and abstract geometric sculptures. [more inside]
posted by Burhanistan on Feb 9, 2008 - 18 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

The Gömböc is the first known convex, homogeneous shape having just one stable and one unstable point (i.e. altogether two points) of equilibrium. A little like some turtles' shells (or weebles), it's self-righting, but for purely geometric reasons. [more inside]
posted by gleuschk on Dec 9, 2007 - 35 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

The Great Pizza Orientation Test.
posted by 31d1 on Oct 24, 2007 - 62 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

Möbius Transformations Revealed [yöutube alert] See also: Stereographic Projection Demo.
posted by chuckdarwin on Jun 26, 2007 - 17 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

STEAM. Australian artist Donna Marcus uses kitchenware to make geodesic spheres to be placed in conspicuous locations.
posted by Burhanistan on Mar 1, 2007 - 16 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

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

Order from chaos! Fill a cylindrical bucket with water and make it so the bottom can spin. At certain speeds, stable regular polygonal shapes will spontaneously form at the turbulent surface of the water. See the video. [2.6MB avi] [via last week's PRL]
posted by sergeant sandwich on May 10, 2006 - 28 comments

Under Foot and Between the Boards in the Laurential Library "Within the Laurentian Library, the enigmatic masterwork of Michelangelo, there exists a complex geometric pavement that is hidden from view, little known about and shrouded with mystery...Why had an immensely complicated pavement been constructed, only to be covered over?"
posted by dhruva on Oct 23, 2005 - 13 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

Euclid in Colour. 'An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid, which range through most of elementary plane geometry and the theory of proportions. What distinguishes Byrne's edition is that he attempts to present Euclid's proofs in terms of pictures, using as little text - and in particular as few labels - as possible. What makes the book especially striking is his use of colour ... '
posted by plep on Aug 11, 2004 - 15 comments

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

This giant Ukrainian Easter Egg (pysanka) was built in 1975 in Vegreville, Canada by (then) Univ. Utah Computer Science Professor Ronald Resch. Interesting egg factoids can be found here--including that it swivels like a weather vane. Vegreville has an annual festival. More images of egg here. The Vegreville Pysanka was the first physical structure completely designed with computer-aided geometric modeling software. There is a good description here of the complex geometry involved. It's based on a technique (PDF) he developed and patented for folding a flat material (i.e. sheet metal) into flexible surfaces. Ronald Resch has had an interesting career.
posted by lobakgo on Apr 8, 2004 - 6 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

'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

The Geometry Center: Center for the Computation and Visualization of Geometric Structures [more]
posted by hama7 on Feb 2, 2003 - 2 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