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"...the answer to Life, the Universe, and Everything is..." "Yes? Yes!?" "...42."

via Dyson, Montgomery, Princeton, a cup of tea - as presented by Seed Magazine.

via Dyson, Montgomery, Princeton, a cup of tea - as presented by Seed Magazine.

Who can name the bigger number? I guarantee you will lose to the Busy Beavers. (No, infinity is not allowed, the bigger infinity is a different game.) The author also debunks in very simple terms the recent story that quantum computers perform calculations without being turned on. My first post and disclaimer: I know the author from our mutual field of quantum information.

The Sarong Theorem Archive is the premier online repository for pictures of mathematicans in sarongs proving theorems.

The Value of Algebra: "*Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers.*"

Ripple Tank Simulation is a delightful, mesmeric java applet simulation of a ripple tank. It demonstrates two dimensional wave phenomena such as interference, diffraction, refraction, resonance, phased arrays, and the Doppler effect (do try the 3D view). From Paul Falstad's fantastic collection of Math, Physics and Engineering Applets.

Oddly obsessive statistical analysis of the rates paid by customers of legal Nevada prostitutes, broken down by sex act, attractiveness, body type and presence or absence of a jacuzzi, among other topics. [via Cynical-C, who swears he found it by accident]

Significance of numbers. Not to be confused with the concept of "significant figures," this page lists the significance of numbers 0 through 1000.
*See!* "2 is the only even prime."
*Hear!* "24 is the largest number divisible by all numbers less than its square root."
*Thrill!* "3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways." Whoa!

Flash Animations for Physics. Animations and interactive demos available in many varieties, such as classical mechanics, nuclear, quantum, and relativistic. There's even a nice explanation of the forces at work in Curling. And if that doesn't wet your geek whistle, then take a peek at the patterns of Visual Math.

Beyond Discovery - illustrations of the path from research to human benefit

A View from the Back of the Envelope - approximations and the fun behind them.

Norman Wildberger's New Trigonometry Dr Norman Wildberger has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. The First chapter of his new book, Divine Proportions, is online (.pdf).

Friday Flash Fun, and other games from the ~~educational~~ entertaining Maths is Fun. Just don't tell the kids they're learning.

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.

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.

Project Euler is a running contest of programming challenges to hone your algorithm skills.
*"Each problem is designed according to a 'one-minute rule', which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute."*

Who has the fish? Einstein logic puzzle. If I can do it, you guys can.

Mathematical proof Mathematical proof that it is impossible to find a girlfriend.
"Without going into the specifics of precisely which traits I admire, I will say that for a girl to be considered really beautiful to me, she should fall at least two standard deviations above the norm." -pdf here- via

Gödel and the Nature of Mathematical Truth : A Talk with Verena Huber-Dyson

The Spidron is an interesting geometric construction that seems to lend itself to folding, dissection, and space-filling in two and three dimensions.

Very few people will ever need to learn the value of pi beyond a handful of digits, but some people are more obsessed than others. They call themselves Piphilologists, and all the pi-memorization writings you could ever possibly want have been compiled into one massive Piphilogical text file. And today, Piphilologists the world over must surely bow in tribute to Akira Haraguchi, who has just recited pi from memory to 83,431 places.

Godel's theorems have been used to extrapolate a great many "truths" about the world. Torkel Franzen sets the record straight in his new book Godel's Theorem: An Incomplete Guide to Its Use and Abuse. Read the introduction (PDF). If you want, check out his explanation of the theorems.

The Logic of Diversity "A new book, *The Wisdom of Crowds* [..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)

Whether its crocheted hyperbolic models or Lorenz manifolds, a lace pi shawl or knit Fibonacci socks, some math geeks find expression in the fiber arts.

That, as previously reported, a newly deciphered fragment of the Book of Revelations shows 616 is the true Number of the Beast, rather than the popular 666, is nothing new in the world of those obsessed with codes in the Bible. However, one Bible code in particular -- Theomatics -- has sparked debate among believers and non-believers alike.

Michael Hutchings' rope trick and Dylan Thurston's two-handed knot-drawing sk1llz. Did you need to kill some time practicing pointless skills today?

Saunders Mac Lane, mathematician, has died, age 95. Winner of the National Medal of Science, Vice-President of the National Academy of Science, President of the American Mathematical Society, author of three of the canonical texts in algebra [reg. maybe req., here's a local copy], Mac Lane was also mathematical ancestor to over a thousand mathematicians, father of category theory and homological algebra, and expert in topology, topos theory, group cohomology, logic, and applied mathematics. He was one of the towering figures of postwar mathematics. Remembered by his students and all of us who were affected by his work and his life.

The Mathematical Fiction Homepage is a collaborative attempt to "collect information about all significant references to mathematics in fiction." Feel free to add classic or recent works in any medium to the collection, or rate existing entries on their mathematical content and literary quality.

Crispin Sartwell is a cryptic and sensational man. The Chair of Humanities and Sciences at the Maryland Institute College of Art, he has translated the Tao Te Ching, published philosophy papers and books, maintained pages on hip hop, founded the American Nihilist Party (and gave a speech to young Democrats urging them to reconsider their votes for John Kerry), taught courses on conjuring and illusion, etc. etc. See also his essay on the pagan cult of mathematics and his thought experiment on music.

The New York City Department of Education has recalled 3rd-7th grade basic math prep materials after finding multiple errors. Like what? Multiplication errors, addition errors, poorly worded questions, and **incorrectly spelling Fourth on the cover of the Fourth Grade Book**. "The fact is, if third- or fifth-grade students made the mistakes made in the test prep materials, they would be flunked and no one would be asking them for an explanation."

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.

Danica McKellar —the former star of The Wonder Years—has her own web site. It's got a great feature where she answers your math questions. No, really. She's got a degree in mathematics and co-authored a paper on percolation and Ashkin-Teller models. No, really.

Hypothesis as thought-crime...Now, however, a new brouhaha has erupted [at Harvard]and it seems impossible that Summers [the president]will emerge from this one without serious erosion of his moral authority. The trigger was a statement he made at a conference, suggesting that the reason there are more men than women in the mathematical sciences at top-flight institutions has to do with a small statistical difference in inate ability, which becomes a pretty large disparity when one looks at the 'high end' of the respective distribution curves...
The fatal words did not set forth his main theme, but merely constituted a brief aside, thoroughly hedged and qualified. Nonetheless, they touched off a firestorm of indignation, the most striking aspect of which was the intemperate response of a number of feminist scientists, who offered no counter-arguments, but simply declared the whole idea misogynistic and therefore forbidden intellectual territory.

Knight's Tour Notes. More than you ever wanted to know about knight's tours on a chessboard.

From MathNet to that silly song about the number nine, Square One was one of my all-time favourite programs as a kid. It hasn't been released on video or DVD, but luckily there are plenty of fansites with video clips, pics, and other media to take you on a trip down mathematical memory lane.

Math And Science Song Information, Viewable Everywhere. For all those times you've needed a catchy acappella tune about doppler shifting *[mp3]* in a hurry, there's now MASSIVE, a fully searchable collaborative database of over 1700 songs about math and science, sponsored in part by the seriously pedagogical Science Songwriters Association. Biz Markie made the cut, and so can you. *[via the always-effervescent Research Buzz]*

The Mathematics Genealogy Project. A service of the Department of Mathematics at North Dakota State University, the project intends to "compile information about ALL the mathematicians of the world. [...] It is our goal to list all individuals who have received a doctorate in mathematics." Seven generations from one of my recent professors back to Gauss, six back to Felix Klein (of Erlangen Program and bottle fame), eight back to Jacobi, and nine back to Poisson and Fourier, then Lagrange, then Euler, then the Bernoulli brothers, then Leibniz, and then it blew up at infinity.

Su Doku. Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. That's all there is to it. It doesn't sound like much, but it's as addictive as hell. The Times is one publication with a daily puzzle (may be unavailable to overseas readers.) There a tuturial and sample puzzle here (flash).

The universe in just two symbols. The rest, as they say, is details. No wonder the "Physics Establishment" is trying to keep this quiet. The author, having conquered the universe in general, tackles poetry, as well.

Minimal surfaces in 3D (red/green, or stereo pairs), with rotate and zoom. If you want to go beyond the eye-candy aspect, here's the obligatory Mathworld link, the classic intuitive explanation, and a raft of additional information. If you *like* eye-candy, don't miss the ray-traced minimal surfaces and these interesting, but non-minimal surfaces.

Thinking Machine 4 *explores the invisible, elusive nature of thought. Play chess against a transparent intelligence, its evolving thought process visible on the board before you.*

From Martin Wattenberg (with Marek Walczak); they have been noted here before.

From Martin Wattenberg (with Marek Walczak); they have been noted here before.

Nick's Mathematical Puzzles. Something to keep you on your toes and exercise your brain this Friday. [not Flash]

Maths puzzles and more problems. Found whilst searching for the fiendish the Monty Hall Problem. A Tangled Tale, indeed.