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520 posts tagged with Math.

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## Freely-available textbooks

## .99999...=1

No, I'm sorry, it does. There are some arguments that never end. John or Paul? "Another thing coming" or "Another think coming?" But none has the staying power of "Is 0.999999...., with the 9s repeating forever, equal to 1?" A high school math teacher takes on all doubters. Round 2. Round 3. Refutations of some popular "They're not equal" arguments. Refutations, round 2. You don't have to a mathematician to get in on the fun: .99999=1 discussed on a conspiracy theory website, an Ayn Rand website (where it is accused to violating the "law of identity"), and a World of Warcraft forum. But never, as far as I can tell, on MetaFilter.

## Scholarpedia

Worried about inaccuracies in Wikipedia? Try Scholarpedia, a peer-reviewed encyclopedia, with articles written by experts in their field. [more inside]

## Life is complex: it has both real and imaginary components

More than fifty selected articles from

*The Princeton Companion of Mathematics*(username:*Guest*, password:*PCM*) — a thematically-organized compendium of mathematics and mathematicians from Fields Medal-winner Tim Gowers. [via, previously]## Mathematics vs. Democracy: A Clear Winner or a Tie Game?

The Marquis de Condorcet and Admiral Jean-Charles de Borda were two men of the French Enlightenment who struggled with how to design voting systems that accurately reflected voters' preferences. Condorcet favored a method that required the winner in a multiparty election to win a series of head-to-head contests, but he also discovered that his method easily led to a paradoxes that produced no clear winners. The Borda method avoids the Condorcet paradox by requiring voters to rank choices numerically in order of preference, but this method is flawed because the withdrawal of a last-place candidate can reverse the election results. Mathematicians in the 19th century attempted to design better voting systems, including Lewis Carroll, who favored an early form of proportional representation. Economist Kenneth Arrow argued that designing a perfect voting system was futile, because his "impossibility theorem" proved that it's impossible to design a non-dictatorial voting system that fulfills five basic criteria of fairness. (more inside)

## "Not without my formula sheets, sir."

Even experts don't know what (3 and 3/16ths) times 20 is. But it has something to do with square roots and kinetic energy. [single link to excellent youtube deposition]

## Möbius strip unravelled

## 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime...

The Prime Game is not really much of a game, but it

*is*a neat & little-known fact about the decimal representation of prime numbers.## ...the models live in the curved space of the hypersphere...

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...

## Snakes, in my heart-blood warm'd, that sting my heart!

SlitherLink - a little spatial-numerical puzzle. Here's a better exposition of the rules from the puzzle's inventors, and another collection of puzzles. Oh, and a little survey of other sneaky, snaky puzzles.

## Math + Vishnu = Really Fast Math

*What is the square of 85? In an instant, a 17-year-old boy said without blinking, "7,225."*

*Kamlesh Shetty had used a trick from a quaint concept called Vedic math, a compilation of arithmetic shortcuts believed to have been written by ancient Indians who lived centuries before Christ, during a glorious period in Indian history called the Vedic Age.*More on Vedic math. Still more. And there's a similar system called the Trachtenberg system, invented in a Nazi concentration camp. Where were these guys when I was in the third grade struggling with my times tables?

## It's math set to music!

The Klein Four is a group of math students at the Northwestern University who delight in bringing you various lovely, well-sung A Capella songs infused with their very own and very nerdy flavour. They're not the newest of the web, having released their first CD in 2005, but witty lyrics and five-part harmonizing are definitely worth checking out. I did do a search for this and didn't find anything. Please don't kill me.

## Mathematics in Movies

## Aptitude Schmaptitude!: innumeracy in America

Aptitude Schmaptitude!

*While the state of mathematical incompetence in this country has been much lamented, most famously in Paulos's brilliant 1988 book Innumeracy, it is still tacitly accepted . . . Being incompetent in math has become not only acceptable in this widely innumerate culture, it has almost become a matter of pride. No one goes around showing off that he is illiterate, or has no athletic ability, but declarations of innumeracy are constantly made without any embarrassment or shame.*## Stonehenge math

Solstice/equinox calculations Been hankering to build your own Stonehenge but got stumped at the planning stage? Paul Doherty shows you the math to construct a modern ancient observatory with angles and facings correct for your latitude.

## The Narrow Road

The Narrow Road : in which a professional mathematician guides you through pure mathematics (and touches on tangential issues).

## by the numbers

Pi to 1,000 places on piano is just one of the many catchy tunes on math sonifications. And check out more interesting things on on artist Tom Dukich's site.

## Math is congruent with fun!

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.

## Golden Ratios

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.]## E8 Structure Decoded

Math Team Solves the Unsolvable E8

"If you thought writing calculations to describe 3-D objects in math class was hard, consider doing the same for one with 248 dimensions. Mathematicians call such an object E

"If you thought writing calculations to describe 3-D objects in math class was hard, consider doing the same for one with 248 dimensions. Mathematicians call such an object E

_{8}, a symmetrical structure whose mathematical calculation has long been considered an unsolvable problem. Yet an international team of math whizzes cracked E_{8}'s symmetrical code in a large-scale computing project, which produced about 60 gigabytes of data. If they were to show their handiwork on paper, the written equation would cover an area the size of Manhattan."## Impossible Crystals

"This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries - such as square, hexagonal and triangular - and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a "quasicrystal," was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials...."

Physicist Paul J. Steinhardt delivers a fascinating lecture (WMV) on tilings and quasicrystals. However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.

Physicist Paul J. Steinhardt delivers a fascinating lecture (WMV) on tilings and quasicrystals. However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.

## My blog is smarter than your blog.

Alain Connes has a blog. Terry Tao also has a blog. Two Fields medalists blog on open problems, their views on mathematics, and Tomb Raider. Timothy Gowers doesn't have a blog, but does have a compendium of informal essays on topics like Why is multiplication commutative? If you prefer pictures to words: Faces of Mathematics.

## Integrals!

The Integrator is Mathematica's integration capabilities, available over the web. Other online resources from Wolfram include Tones, an automatic music generator, and the venerable Mathworld, an extensive collection of math terms and theorems. (which, yes, has been mentioned previously.)

## Graphs

## Seb Przd's mind-bending photos

Seb Przd's photos specialising in delightful and mind-bending spherical panoramas and conformal mappings.

## Physics simulators. Lots of physics simulators.

PhET - Physics Education Technology offers this astoundingly large library of online physics simulations. Play orbital billiards. Land on a cheesy moon. Experiment with sound. Or try more advanced quantum physics simulators. Still bored? Try the "cutting edge" catagory. Here's the complete index. (Warnings: Frames, Flash, Javascript, Java applets, graphics, sound, quantum timesuck.)

## In Soviet Russia, sponge soaks you

Dr. Jeannine Mosely finishes building a level-3 Menger sponge from business cards. You can also build your own, though Dr. Mosely warns, "[a] level 4 sponge would require almost a million cards and weigh over a ton. I do not believe it could support its own weight — so a level 3 is the biggest sponge we can hope to build." (related)

## Ben Laposky, the Father of Computer Art?

Pioneering electronic artist Ben Laposky began creating his “Oscillons” – abstract artworks created by photographing Lissajous figures off a cathode-ray oscilloscope – in the early 1950’s. Some consider him the father of computer art, and the beauty and clarity of his work is astonishing.

## Math + eggs = yum(n^n+1)

## Operation Kaprekar

Mysterious number 6174. An excellent recreational math article.

## Gallery

## $0.002 != $0.00002

Math skills are not Verizon's strong point. A man tries to resolve a simple problem with Verizon for 22 minutes. Listen, and despair.

## Nullity and Perspex Machines

Dr James Anderson, from the University of Reading's computer science department, claims to have defined what it means to divide by zero. It's so simple, he claims, that he's even taught it to high school students [via Digg]. You just have to work with a new number he calls Nullity (RealPlayer video). According to Anderson's site The Book of Paragon, the creation, innovation, or discovery of nullity is a step toward describing a "perspective simplex, or perspex [ . . . ] a simple physical thing that is both a mind and a body." Anderson claims that Nullity permits the definition of transreal arithmetic (pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue No Zombies, Only Feelies? identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined.

## Mandelbrot on Fractals as A Theory of Roughness.

A talk with Benoît Mandelbrot, entitled Fractals in Science, Engineering and Finance (Roughness and Beauty) [video, 80mins, realplayer] about fractals as A Theory of Roughness.

## Geek Logik - math for every day

Geek Logik is Garth Sundem's book & blog about equations for every day living, including how many cups of coffee you require to be functional, who to vote for, and others.

## Raft to the Future

Raft to the Future: An article about the weirdness of physical models of the universe, how that weirdness correlates to the inherent incompleteness of mathematical systems, and how time itself can

*emerge*at the fringes of these incomplete models.## Fractran.

Fractran. A Turing complete programming language expressed in prime numbers from John Conway. (Interpreter here.) More pathological programming. Via Good Math, Bad Math.

## pi in pixels

what happens if you assign a colored pixel to each decimal of pi?

## Another Clay Institute Millenium Prize Problem Solved?

The Navier-Stokes equations constitute the fundamental equations that describe fluid mechanics, and are used everywhere from atmospheric science to airplane design. Proof of the existence of a smooth solution to the Navier-Stokes equations in 3-dimensions is considered a challenging problem, so challenging that the Clay Math Institute has offered a million dollars to anyone who can do so. Has it been done? (More detailed explanation). (via)

## crocheted hyperbolic flora and fauna

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)

## Interview of Grigory Perelman

Grigory Perelman, awarded the Fields Medal for his work on the Poincare Conjecture, talks to the New Yorker.

## random(1-100)

Please pick a random number between 1 and 100 (Explanation follows after filling out a short form.)

## никакое спасибо

Grigory Perelman becomes first to reject Fields Medal:

*"I do not think anything that I say can be of the slightest public interest. I have published all my calculations. This is what I can offer the public."*Perelman was to be awarded the medal due to his solution of the Poincaré Conjecture. More on the other winners. Via.## Every spherical football is a branched cover of the standard one.

Bending a soccer ball - mathematically. Found via Ivars Peterson's short exposition on Braungardt and Kotschick's The Classification of Football Patterns [pdf, technical].

## Things you didn't know about Bruce Schneier. They are on the internet, so they must be true.

## paging dr. perelman

Grisha Perelman, where are you? Perelman has quite possibly solved one of mathematics biggest mysteries, Poincaré’s conjecture, but has since disappeared.

## 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".