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## More than you ever wanted to know about nothing at all

The Zero Saga contains a great deal of information about the concept of zero, and its relation to other numbers and concepts in mathematics. It was linked in Good Math, Bad Math; which contains a variety of other informative articles on the numbers that capture our imaginations. (

**Note:**You may want to skip past part 4 of the Zero Saga, as it contains replies to the site, and as such should probably be at the bottom of the page. But, to compensate, the comments on Good Math are better than most blogs I've read.)## Minimum sudoku

Minimum Sudoku. It is believed (though not proven) that the minimum number of entries in a Sudoku grid that will lead to a unique solution is 17. Gordon Royle of the University of Western Australia has collected 36,628 "minimum Sudoku" grids. Additional reading: an article in American Scientist on determining the difficulty of a Sudoku problem; Wikipedia article on the mathematics of Sudoku; the Sudoku Programmers' Forum on Sudoku mathematics.

## Mathematical imagery by Jos Leys.

Sphere and circle arrangements, the Droste effect, and more: mathematical imagery by Jos Leys. The Droste effect article is informative, too.

## Pianolina

The Pianolina - an addictive flash game - is something like a cross between Pong and WolframTones. Brought to you by Grotrian, piano manufacturers since 1835, the pianolina visualizes musical notes as little squares that chime when they bounce against each other or against a wall. Its sophisticated interface lets you add chords, gravity, or start with the basic notes of well known compositions like Beethoven's "Für Elise".

## ^_* *_^

## Mapping the StarMaze

Mapping the StarMaze A tale of mathematical obsession: "Before I can explain my decades-long quest to map the starmaze I must acquaint you with a small puzzle...I have a habit of seeing everything (cities, organizations, computers, networks, brains) as a maze, so I named this puzzle the starmaze....The first problem I ran into was that there were a lot of rooms...I invented wacky names for each room...But something funny happened...In that instant I finally grasped that the starmaze was arranged on the edges of a nine-dimensional hypercube..."

## A Romance in Lower Mathematics.

## Show Your Work

Condoleezza holds a watermelon just over the edge of the roof of the 300-foot Federal Building, and tosses it up with a velocity of 20 feet per second. Using the formula provided, when the watermelon will hit the ground? Bellevue Community College President Jean Floten asked the Pluralism Steering Committee to take the lead on this, and to complete their task quickly.

## Butt formula

## Meta Math

Gregory Chaitin's Meta Math! The Quest For Omega

"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness.

"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings.

[previously, see also, via]

"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness.

"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings.

[previously, see also, via]

## This Week's Finds in Mathematical Physics

This Week's Finds in Mathematical Physics. A geek's paradise. Reminiscent of Scientific American's

*Mathematical Games.*## ...almost, but not quite, entirely unlike tea.

"...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?

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.

## Sarong Theorem Archive

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

## MathFilter(edout)

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

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.

## Bashful's prostitution survey

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]

## Klik Kandy

## Significant numbers

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!## Nerd Porn

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.

## Tangible Applications of Science

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

## Guess about 2 people will snark about this title

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

## Sine of the times

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).

## Is our children learning maths?

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

## Math You Don't Know, and Math You Didn't Know You Didn't Know.

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.

## Java applets to help visualize various concepts in math, physics, and engineering

## What kind of a sculpture would Metafilter represent?

## Euler? I never even met her!

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."*## Mathematical Knitting.

## Who has the fish?

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

## Finding a girlfriend is a impossible - the proff

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

## Nature of Mathematical Truth

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

## Just filling space

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

## 3.1415926535897932384626433...

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.

## You can't prove this title wasn't an attempt to illustrate Godel

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.

## Danica Mckellar eat your heart out

## The Complexity of a Controversial Concept

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)## Crafty geeks

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.

## Let's get stoned and explore bounded equations

## Ow, my brain hurts!

## What do you call a young eigensheep?

## 616, 666 and other Bible math

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.

## No, I'm a frayed knot

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, 1909--2005

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.

## 1 + 2 = high drama

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.

## MathematicsFilter

## Thoroughly Rehearsed Human Combustion

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.

## 1 + 1 = 2. Really. Honestly.

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."## Fun With Geometry

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.

## Winnie Knows Math

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.