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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

Euclid is a game of geometry played in your browser.

posted by boo_radley on Jun 20, 2014 - 71 comments

posted by boo_radley on Jun 20, 2014 - 71 comments

Spherical Voronoi diagram of world airports [more inside]

posted by Wolfdog on May 8, 2014 - 42 comments

posted by Wolfdog on May 8, 2014 - 42 comments

Polyhedra and the Media - On the new polyhedra of Schein and Gayed, and mathematical journalism.

posted by Wolfdog on Mar 11, 2014 - 20 comments

posted by Wolfdog on Mar 11, 2014 - 20 comments

Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]

posted by Elementary Penguin on Feb 22, 2014 - 10 comments

posted by Elementary Penguin on Feb 22, 2014 - 10 comments

Visual Patterns. Here are the first few steps. What's the equation?

posted by Wolfdog on Feb 18, 2014 - 19 comments

posted by Wolfdog on Feb 18, 2014 - 19 comments

The Hierarchy of Hexagons. *School geometry seems to me one of the most lifeless topics in all of mathematics.
And the worst of all? The hierarchy of quadrilaterals.*

posted by Wolfdog on Feb 11, 2014 - 36 comments

posted by Wolfdog on Feb 11, 2014 - 36 comments

A standard 6 sided die is a cube. It has eleven nets. The sum of the numbers on opposite faces of a die is 7. [more inside]

posted by Elementary Penguin on Jan 30, 2014 - 26 comments

posted by Elementary Penguin on Jan 30, 2014 - 26 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

PORCELAINia. A short documentary about artist and scientist Bobby Jaber. [Via]

posted by homunculus on Aug 4, 2013 - 5 comments

posted by homunculus on Aug 4, 2013 - 5 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

People have long been interested in the architectural endeavors of animals. The internal structure of bee hives, the hexagonal combs of wax, have been amongst these ponderings, going back to Marcus Terentius Varro's *Rerum Rusticarum Libri Tres*, a volume on
Roman farm management. He wrote, "The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space," and over the years, mathematicians have studied the hexagonal structures made by bees, and in 1998, Thomas Hales produced a mathematical proof for the classical hexagonal honeycomb conjecture, which "asserts that the most efficient partition of the plane into equal areas is the regular hexagonal tiling." [more inside]

posted by filthy light thief on May 21, 2013 - 25 comments

posted by filthy light thief on May 21, 2013 - 25 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

Emma Kunz was a telepathic healer and researcher. Even though she didn't consider herself an artist, the hypnotic symmetry found in her hand-drawn healing charts is breathtaking.

posted by shackpalace on Jan 6, 2013 - 36 comments

posted by shackpalace on Jan 6, 2013 - 36 comments

The Royal Spanish Library has put online today an interactive version of Leonardo da Vinci's Madrid Codices I & II. There are transcriptions of the text (in Spanish and Italian, click "T" on the bottom menu), animations of many of the mechanical contraptions (click play button "ver animacion") and the "Indice" in the bottom menu organizes the folios by theme.

posted by Marauding Ennui on Oct 30, 2012 - 3 comments

posted by Marauding Ennui on Oct 30, 2012 - 3 comments

To keep yourself amused during your math class, you start playing with [all these strips of paper]. And by you, I mean Arthur H. Stone in 1939. (SLYT)

posted by 256 on Oct 1, 2012 - 35 comments

posted by 256 on Oct 1, 2012 - 35 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

Liam Brazier uses geometric shapes to create neat illustrations of pop-culture icons. [more inside]

posted by quin on Aug 13, 2012 - 5 comments

posted by quin on Aug 13, 2012 - 5 comments

A large selection geometric shapes, all created with just one HTML element & CSS. An interesting take on geometry. Includes Space Invader. [more inside]

posted by Deathalicious on May 30, 2012 - 31 comments

posted by Deathalicious on May 30, 2012 - 31 comments

Animated projections of the hyperbolic plane. The author also makes jewelry, sculptures.

posted by phrontist on Mar 12, 2012 - 14 comments

posted by phrontist on Mar 12, 2012 - 14 comments

Man Walks All Day to Create Spectacular Snow Patterns

posted by signal on Feb 24, 2012 - 22 comments

posted by signal on Feb 24, 2012 - 22 comments

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

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

posted by escabeche on Oct 19, 2011 - 29 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

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

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

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

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

Geometry, Surfaces, Curves, Polyhedra (many of which are beautiful) l Google Earth Fractals l fractals and chaos. [more inside]

posted by nickyskye on Nov 1, 2010 - 5 comments

posted by nickyskye on Nov 1, 2010 - 5 comments

When he was 32, his life seemed hopeless. He was bankrupt and without a job. He was grief stricken over the death of his first child and he had a wife and a newborn to support. Drinking heavily, he contemplated suicide. Instead, he decided decided that his life was not his to throw away: it belonged to the universe. Buckminster Fuller embarked on "an experiment to discover what the little, penniless, unknown individual might be able to do effectively on behalf of all humanity." If the architect, author, designer, inventor, and futurist Richard Buckminster "Bucky" Fuller were still alive, he would be 115 years old today. Though he died in 1983, his legacy grows on through recordings of his ideas and the Buckminster Fuller Institute. [more inside]

posted by filthy light thief on Jul 12, 2010 - 32 comments

posted by filthy light thief on Jul 12, 2010 - 32 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

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

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

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

posted by Burhanistan on Aug 6, 2009 - 31 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

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

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

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

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

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

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

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

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

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

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

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

posted by parudox on Dec 1, 2007 - 11 comments

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