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368 posts tagged with Mathematics.

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## Operation Kaprekar

Mysterious number 6174. An excellent recreational math article.

## Gallery

## 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.

## Good times, good times!

Autodidactic goodies on a budget: Free computer books and online lectures, seminars and instructional materials from a variety of renowned institutions.

## Of course, I'm illiterate!

Platonic Realms is an online math academy. It features a searchable encyclopedia with extended articles on things from Cantor's Theorem to Zeno's Paradox of the Tortoise and Achilles. You'll also find minitexts, such as "Coping with Math Anxiety" and "The Mathematical Art of M.C. Escher". Last but not least, a searchable math quotes database.

## Sorry, but I can't find "Story of Your Life"

## Interview of Grigory Perelman

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

## Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning

Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning [video] "The picture is a telescope for looking into Plato's heaven." -- James Brown [cached]

## 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.

## Turing: The Final Years

Among his collected works, in the few, short years before mathematician Alan Turing was driven to suicide, he published

*"The Chemical Basis of Morphogenesis"*, theorizing how a standing wave-like distribution of "cannibal" and "missionary" chemicals might explain how plants and animals develop their shape and pigmentation. Blogger Jonathan Swinton focuses on this more obscure aspect of Turing's research, and reviews some of his posthumous and unpublished efforts — including one of the earliest known examples of digital computation applied to the field of biology.## 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.)## The Moving Sofa Constant

The Moving Sofa Constant. We have noticed you have a small personal problem with sofas. You move them and get them stuck in hallways. But it's nothing a little math won't fix.

## 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.

## divide and conquer

Math gets a patent.

"The field of invention relates generally to performing division operations using processing components and, more specifically but not exclusively relates to techniques for performing efficient software-based integer division using reciprocal multiplication."

"The field of invention relates generally to performing division operations using processing components and, more specifically but not exclusively relates to techniques for performing efficient software-based integer division using reciprocal multiplication."

## 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.

## The Difference Engine

Charles Babbage's Difference Engines. One built in 1853. A subsequent design completed in 1991. And again in Lego. Both designs recreated in Meccano parts. [more inside]

## ...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.

## 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.*"## It's all a numbers game...

## noe .2. thynges, can be moare equalle.

*"To avoide the tediouse repetition of these woordes: is equalle to:*

*I will settle as I doe often in woorke use, a paire of paralleles, or gemowe lines of one lengthe: ======, bicause noe .2. thynges, can be moare equalle."*Welsh mathematician Robert Recorde (1510–1558) invented the equals sign in his 1557 work

*The Whetstone of Witte*, which also introduced "Zenzizenzizenzic", the eighth power of a number. Recorde had advocated the + and – symbols in his 1540 work

*The Grounde of Artes*. He died in debtor's prison in 1558. Read, watch, or listen to a recent lecture that links the equals sign to developments in art, navigation, and astronomy. (Wikipedia)

## "Face the face, got to face the face"

An awkward resemblance to a certain eigenface might get you pulled aside in Las Vegas. Prof. Hilbert is probably spinning in his grave.

## "This ain't no disco/This ain't no foolin' around"

Mathematical proofs

*in sanus*, with some visualization from Martin Wattenberg's The Shape of Song. "The music here...is a raw and unadorned representation of the mathematics itself, involving few human preconceptions beyond a basic mapping needed to accommodate the Western tonal scale."## How to Draw a Straight Line

How to Draw a Straight Line - Until 1873, virtually all mathemeticians and engineers agreed that it was impossible to build a linkage that could convert circular motion to perfectly straight motion. In that year, Lipmann Lipkin rediscovered the Peaucellier cell which had been quietly created a decade earlier. Although much simpler to build, it was predated by Pierre-Frederic Sarrus' non-planar solution. Nowadays, though, linkages can do some extremely complex things. (via)

## 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.

## Lost and Found

Not Lost After All Given recent posts proving and disproving various meanings of the ongoing numbers references on the television program Lost, I figured that some of you would be interested that a person over on Flickr seems to have a much better explanation: they're simply geographic coordinates.

## 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).

## 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.

## What kind of a sculpture would Metafilter represent?

## Negative knowledge (or more precisely negative information)

Know less than nothing!?

*What could negative knowledge possibly mean? In short, after I tell you negative information, you will know less...*"In this week's issue of Nature, however, Michal Horodecki and colleagues present a fresh approach to understanding quantum phenomena that cannot be grasped simply by considering their classical counterparts." [via slashdot :]## The World is Bound With Secret Knots

Athanasius Kircher was the 17th century's Jesuit version of the

*über*geek. His scholarly attentions were drawn to egyptology, astronomy, magnetism, languages, optics, music, geology, mathematics and many many other pursuits. The "dude of wonders" invented novel machines such as the mathematical organ and magnetic clock, established one of the first museums, published about 40 academic works (with beautiful accompanying illustrations) and was globally revered as one of his time's greatest intellectuals. He is also the main link in the Voynich manuscript mystery. [**MI**]## MARGE! You're soaking in it!

Fractal animation videos. Tune in. Turn on. Drop in on a dripping skirling-swirling pulsating orgy of self-transforming recursive math. Some with fractal music. (Non-embedded mpeg-1 and mpeg-2 files, like God intended.)

## Nature of Mathematical Truth

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

## 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.

## 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)## What makes a hat into hate?

That's Mathematics! Warning, contains bad camera work, worse editing, a rather complicated homework problem, a few mathematical in-jokes, illegible chalkboard writing, and a 13 minute performance by Tom Lehrer.

## 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

## Capturing the Unicorn

Capturing the Unicorn : How two mathematicians helped the Met to digitally stitch together the Unicorn Tapestry. (via)

## 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

## To “have the privilege of walking home with Gödel.”

“Gödel put logic on the mathematical map.”

An excellent interview with Rebecca Goldstein, biographer of Kurt Godel

An excellent interview with Rebecca Goldstein, biographer of Kurt Godel

## 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.

## snow sculpture

Mathematical Model : Knot Divided at the Budweiser International Snow Sculpture Championships 2005. Previous Mefi discussion.

## Hypothesis as thought-crime

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.

## MetaMath

+Plus - An internet magazine published five times a year which aims to introduce readers to the beauty and the practical applications of mathematics.

## Game Theory Resource

## The Mathematics Genealogy Project

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.