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Middle East Peace Potential through Dynamics in Spherical Geometry: Engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks. * This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism...Mathematically these patterns cannot be readily combined. This issue is described in mathematics in terms of tiling...A set of hexagons and pentagons can however be uniquely fitted together as a particular three-dimensional polyhedron, namely the truncated icosahedron. * [more inside]

posted by leahwrenn on Aug 21, 2014 - 29 comments

posted by leahwrenn on Aug 21, 2014 - 29 comments

The Peg Solitaire Army is a problem spun off from a classic recreation, and yet another example of the golden ratio turning up where you least expect it. If you want to look at the game more deeply, George Bell's solitaire pages are the ne plus ultra: There's more about the solitaire army (and variants), ... [more inside]

posted by Wolfdog on Aug 15, 2014 - 6 comments

posted by Wolfdog on Aug 15, 2014 - 6 comments

Welcome to Al Zimmermann's Programming Contests. *You've entered an arena where demented computer programmers compete for glory and for some cool prizes.* The current challenge is just about to come to an end, but you can peruse the previous contests and prepare for the new one starting next month.

posted by Wolfdog on Aug 14, 2014 - 11 comments

posted by Wolfdog on Aug 14, 2014 - 11 comments

The 2014 Fields Medals have been awarded to Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani. Mirzakhani, a professor at Stanford, is the first woman to win math's highest prize, and Avila is the first South American. Erica Klarreich at Quanta Magazine has profiles of all four winners. [more inside]

posted by escabeche on Aug 12, 2014 - 35 comments

posted by escabeche on Aug 12, 2014 - 35 comments

The power of math: 17 Equations That Changed the World - a one table summary of the book by Ian Stewart FRS. Business Insider gives its interpretation of the importance of each equation. Brain pickings (2012) on this book and equations, and another extract from the book. [more inside]

posted by Wordshore on Aug 10, 2014 - 36 comments

posted by Wordshore on Aug 10, 2014 - 36 comments

The Foehr Reef is part of the worldwide Crochet Coral Reef Project. It was made by over 700 women and combines more than 4000 individual pieces of marine wonder. A short video shows its beauty [alternating English and German audio]. PDFs with pictures.
"The Crochet Coral Reef is a woolly celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world." It originated out of a desire to increase awareness of environmental threats to the world's reefs and is a conjunction of art, environmentalism, and geometry. [more inside]

posted by travelwithcats on Aug 10, 2014 - 7 comments

posted by travelwithcats on Aug 10, 2014 - 7 comments

"An unusual article recently appeared in the magazine of the Royal Statistical Society and American Statistical Association.
It featured web-like diagrams of lines connecting nodes, a hallmark of research that analyzes networks. But each node, rather than being a plain dot, was the head of a burly, red-bearded Viking sporting a horned hat, his tresses blowing in the wind." [more inside]

posted by gingerbeer on Jul 18, 2014 - 11 comments

posted by gingerbeer on Jul 18, 2014 - 11 comments

Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again) - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named Claude Shannon." [more inside]

posted by kliuless on Jul 11, 2014 - 12 comments

posted by kliuless on Jul 11, 2014 - 12 comments

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

Visualizing Algorithms shows you how computer algorithms can be represented visually, leading to better understanding of how the algorithms work:

"Have you ever implemented an algorithm based on formal description? It can be hard! Being able to see what your code is doing can boost productivity. Visualization does not supplant the need for tests, but tests are useful primarily for detecting failure and not explaining it. Visualization can also discover unexpected behavior in your implementation, even when the output looks correct."

posted by quiet earth on Jun 26, 2014 - 29 comments

"Have you ever implemented an algorithm based on formal description? It can be hard! Being able to see what your code is doing can boost productivity. Visualization does not supplant the need for tests, but tests are useful primarily for detecting failure and not explaining it. Visualization can also discover unexpected behavior in your implementation, even when the output looks correct."

posted by quiet earth on Jun 26, 2014 - 29 comments

Scott Aaronson on building a 'PageRank' for (eigen)morality and (eigen)trust - "Now, would those with axes to grind try to subvert such a system the instant it went online? Certainly. For example, I assume that millions of people would rate Conservapedia as a more trustworthy source than Wikipedia—and would rate other people who had done so as, themselves, trustworthy sources, while rating as untrustworthy anyone who called Conservapedia untrustworthy. So there would arise a parallel world of trust and consensus and 'expertise', mutually-reinforcing yet nearly disjoint from the world of the real. But here's the thing: *anyone would be able to see, with the click of a mouse, the extent to which this parallel world had diverged from the real one*." [more inside]

posted by kliuless on Jun 23, 2014 - 45 comments

posted by kliuless on Jun 23, 2014 - 45 comments

The Altgeld Math Models. Below you will find around 170 of the models that were photographed in March 2005 when the third floor model cases had to be emptied and moved. The models were carefully moved into the undergraduate lounge and arranged in a miniature "model museum" for two weeks, where each was carefully photographed and is now available for your enjoyment below. [more inside]

posted by obscurator on Jun 3, 2014 - 11 comments

posted by obscurator on Jun 3, 2014 - 11 comments

Who or what broke my kids? "The basic premise of the activity is that students must sort cards including probability statements, terms such as unlikely and probable, pictorial representations, and fraction, decimal, and percent probabilities and place them on a number line based on their theoretical probability. I thought it would be an interactive way to gauge student understanding. Instead it turned into a ten minute nightmare where I was asked no less than 52 times if their answers were “right”. I took it well until I was asked for the 53rd time and then I lost it. We stopped class right there and proceeded to have a ten minute discussion on who broke them."

posted by escabeche on Jun 1, 2014 - 107 comments

posted by escabeche on Jun 1, 2014 - 107 comments

Five reasons not to share that Common Core worksheet on Facebook [more inside]

posted by eviemath on May 25, 2014 - 202 comments

posted by eviemath on May 25, 2014 - 202 comments

I was surprised to learn that few people knew that almost all maths was written rhetorically before the 16th century, often in metered poetry. Even our wonderful symbol for equality – you know, those two parallel lines – was not used in print before 1575.

posted by sammyo on May 24, 2014 - 39 comments

posted by sammyo on May 24, 2014 - 39 comments

Math or Maths? A few minutes with Dr Lynne Murphy (an American linguist in England) should clear this right up. Via Numberphile.

posted by R. Mutt on Apr 30, 2014 - 116 comments

posted by R. Mutt on Apr 30, 2014 - 116 comments

“I wanted to use the intermediate value theorem but it just wasn’t happening.” MIT undergrad Zach Wener-Fligner reports from this year's William Lowell Putnam Mathematical Competition, the nation's premier math contest for college students, a test so hard that the median score is often zero.

posted by escabeche on Apr 27, 2014 - 38 comments

posted by escabeche on Apr 27, 2014 - 38 comments

Can you ever be reasonably sure that something is random, in the same sense you can be reasonably sure something is not random (for example, because it consists of endless nines)? Even if a sequence looked random, how could you ever rule out the possibility that it had a hidden deterministic pattern? And what exactly do we mean by “random,” anyway?

posted by empath on Apr 24, 2014 - 48 comments

posted by empath on Apr 24, 2014 - 48 comments

Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)

posted by kliuless on Apr 12, 2014 - 24 comments

posted by kliuless on Apr 12, 2014 - 24 comments

Based on the Wheat and Chessboard problem, the Chess Board Clock is "a binary clock counting down 2 to the 63rd power in hundredths of a second". The first few squares go by super fast (a non-seizure mode is available) while the last square won't be reached for over 2 billion years. [via mefi projects]

posted by divabat on Apr 3, 2014 - 15 comments

posted by divabat on Apr 3, 2014 - 15 comments

Arthur C. Clarke, Benoit Mandelbrot, Stephen Hawking, David Gilmour and many more trip the fuck out about Fractals, the Colors of Infinity.

posted by loquacious on Apr 3, 2014 - 19 comments

posted by loquacious on Apr 3, 2014 - 19 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

Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)

posted by kliuless on Mar 9, 2014 - 15 comments

posted by kliuless on Mar 9, 2014 - 15 comments

The Teaching of Arithmetic: The Story of an experiment. *In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - my new Three R's. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language. I picked out five rooms - three third grades, one combining the third and fourth grades, and one fifth grade. I asked the teachers if they would be willing to try the experiment.*

posted by Wolfdog on Mar 8, 2014 - 18 comments

posted by Wolfdog on Mar 8, 2014 - 18 comments

Discovering Free Will (Part II, Part III) - a nice discussion of the Conway-Kochen "Free Will Theorem". [more inside]

posted by Wolfdog on Mar 4, 2014 - 92 comments

posted by Wolfdog on Mar 4, 2014 - 92 comments

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of *understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)

posted by kliuless on Mar 2, 2014 - 17 comments

posted by kliuless on Mar 2, 2014 - 17 comments

You Should Always Get the Bigger Pizza (SL NPR blog post w/interactive graph)

posted by neroli on Feb 28, 2014 - 154 comments

posted by neroli on Feb 28, 2014 - 154 comments

Astroblast and Overstepping Artifacts are music videos by the project Musicians with Guns, which take the viewer through detailed tours of some beauty. Relax and enjoy.

posted by Blazecock Pileon on Feb 27, 2014 - 9 comments

posted by Blazecock Pileon on Feb 27, 2014 - 9 comments

Each month, the Notices of the American Math Society runs a column called "What is...." which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good undergrad math major. Armin Straub, a postdoc at Illinois, has collected them all in one place. [more inside]

posted by escabeche on Feb 26, 2014 - 33 comments

posted by escabeche on Feb 26, 2014 - 33 comments

Reaction-diffusion reactions used to design housewares, puzzles, and more. If you want to experiment yourself, you might get some ideas from the demos at WebGL Playground or you might use this brief intro as a jumping-off point.

posted by Wolfdog on Feb 23, 2014 - 13 comments

posted by Wolfdog on Feb 23, 2014 - 13 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

Open warfare erupts in the world of mathematical biology, as Lior Pachter of UC-Berkeley writes three blog posts attacking two papers in Nature Bioscience, accusing one of them of being "dishonest and fraudulent": The Network Nonsense of Albert-Laszlo Barabasi, The Network Nonsense of Manolo Kellis, and Why I Read the Network Nonsense Papers. Kellis (MIT) and his co-authors respond (.pdf.)

posted by escabeche on Feb 12, 2014 - 53 comments

posted by escabeche on Feb 12, 2014 - 53 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

What would happen if a cue ball struck a rack of 15 perfectly round, frictionless billiard balls, exactly head-on?

posted by escabeche on Feb 3, 2014 - 31 comments

posted by escabeche on Feb 3, 2014 - 31 comments

How a Math Genius Hacked OkCupid to Find True Love

posted by kyp on Jan 21, 2014 - 101 comments

“I think that what I did is just a slightly more algorithmic, large-scale, and machine-learning-based version of what everyone does on the site,” McKinlay says. Everyone tries to create an optimal profile—he just had the data to engineer one.[more inside]

posted by kyp on Jan 21, 2014 - 101 comments

M.I.T. professor Max Tegmark explores the possibility that math does not just describe the universe, but makes the universe.

posted by COD on Jan 14, 2014 - 111 comments

posted by COD on Jan 14, 2014 - 111 comments

1 + 2 + 3 + 4 + 5 ... = -1/12 -- Numberphile explains a counter-intuitive summation of an infinite series. [more inside]

posted by empath on Jan 9, 2014 - 136 comments

posted by empath on Jan 9, 2014 - 136 comments

"The IPython Notebook is a web-based interactive computational environment where you can combine code execution, text, mathematics, plots and rich media into a single document". It can be installed faily easily with anaconda or on Amazon EC2.
Various interesting notebooks are to be found at the official Notebook Viewer site
Another collection of interesting notebooks on many topics. [more inside]

posted by meta87 on Jan 5, 2014 - 56 comments

posted by meta87 on Jan 5, 2014 - 56 comments

It's a bit late for the holiday, but math(s) comedian Helen Arney sings about her Christmas wish -- the largest known Mersenne Prime, Mersenne 48. [more inside]

posted by GenjiandProust on Dec 28, 2013 - 1 comment

posted by GenjiandProust on Dec 28, 2013 - 1 comment

According to statistician Aki Vehtari of Aalto University in Finland, there is diminished 20% chance that today, December 25th, is your birthday. There is a 5% higher likelihood than chance that your birthday is actually February 14th. [more inside]

posted by roomthreeseventeen on Dec 25, 2013 - 27 comments

posted by roomthreeseventeen on Dec 25, 2013 - 27 comments

Try to defeat the hydra! (Java required.) More about hydra math.

posted by divabat on Dec 22, 2013 - 27 comments

posted by divabat on Dec 22, 2013 - 27 comments

Charan Langton (blog) hosts Complex To Real: which "...offers tutorials I have written on various topics in analog and digital communications that will help you cut through this complexity." [more inside]

posted by Confess, Fletch on Dec 21, 2013 - 8 comments

posted by Confess, Fletch on Dec 21, 2013 - 8 comments

531 of the most interesting articles on Wikipedia covering everything from the linguistic (self-contradicting words in English) to the philosophical (The Ultimate 747 Gambit); from the only German military landing in the Americas (Weather Station Kurt) to the world's only Bigfoot Trap; to oddities both geometric (Gömböc ) and mathematical (Tupper's self-referential formula); great lists of various things (Bible errata, unsolved problems, camouflage patterns, blurred spots on Google Maps, lost art, the last monarchs of the Americas) to things that will make great band names (Orbiting Frog Otolith). [prev, shorter lists]

posted by blahblahblah on Dec 14, 2013 - 17 comments

posted by blahblahblah on Dec 14, 2013 - 17 comments

Watching one of the exciting snow-bound football games yesterday, the thought may have occurred to you: If I was a coach, would I go for it on this 4th down? This bot from the New York Times will tell you, and maybe even add a little attitude to the answer, which is usually much more aggressive than NFL coaches.

posted by Potomac Avenue on Dec 9, 2013 - 74 comments

posted by Potomac Avenue on Dec 9, 2013 - 74 comments

Recently Emily Graslie, of the fantastic natural history tumblr and youtube series TheBrainScoop, was asked a question about whether she had personally experienced sexism in her field. Her response is fucking amazing.

posted by Blasdelb on Dec 6, 2013 - 37 comments

Inside is her goldmine of awesome female science educators online with channels that focus on Science Technology Engineering and Math. My work day is fucked.[more inside]

posted by Blasdelb on Dec 6, 2013 - 37 comments

Headlines from a Mathematically Literate World [more inside]

posted by Blasdelb on Dec 4, 2013 - 32 comments

posted by Blasdelb on Dec 4, 2013 - 32 comments