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559 posts tagged with Math.

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## Topology on the Runway

There's always been hyperbole in fashion; but fashion became truly hyperbolic this week when mathematican William Thurston, winner of a 1982 Fields Medal for his revolutionary re-envisioning of low-dimensional topology and geometry, teamed up with designer Dai Fujiwara (of the house of Issey Miyake) to produce a Paris runway show based on the fundamental geometries of 3-dimensional spaces. Thurston and Fujiwara briefly interviewed. Thurston's famous essay "Proof and Progress in Mathematics" concerns, among other things, Thurston's belief that the production of mathematical understanding can be carried out by means other than the writing down of formal proofs (though fashion shows are not specifically mentioned.) Previously in wearable non-Euclidean geometry: Daina Taimina's hyperbolic skirt.

## How the cortex got its stripes

Uncoiling the spiral: Maths and hallucinations

*So common are these geometric hallucinations, that in the last century scientists began asking themselves if they couldn't tell us something fundamental about how our brains are wired up. And it seems that they can.*(via MAPS)## Math class is hard.

*Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers’ anxieties relate to girls’ math achievement via girls’ beliefs about who is good at math.*A study (abstract and full-text [pdf]) by the University of Chicago Department of Psychology and Committee on Education found a link between math anxiety in elementary school teachers and their female students' math abilities. [more inside]

## Contact is the secret, is the moment, when everything happens. Contact....

From 1980 - 1988, a science education series called 3-2-1 Contact ran on PBS. Produced by Children's Television Workshop, the series was geared toward an older audience than other popular CTW offerings Sesame Street and The Electric Company, and focused on teaching kids about science, math and the world around them. [more inside]

## Nontransitive dice

Nontransitive dice are sets of dice (A, B, C, etc.) with counterintuitive properties: die A beats die B and die B beats die C, but die C beats die A. [more inside]

## All Gnytte Long

The Sexaholics of Truthteller Planet - yes, it's one of those rotten logic problems, one of many that can be found at Tanya Khovanova’s Math Guide to the MIT Mystery Hunt.

## Lun-Yi Tsai

## Calculus of Averages

Calculus of Averages -

*Newton and Archimedes did not possess this knowledge. No mathematics professor today can provide this knowledge and depth of understanding.*Author John Gabriel maintains a blog, Friend of Wisdom, and contributes articles such as Are real numbers uncountable? to Google's Knol project.## The beauty of roots

The beauty of roots. From Dan Christensen and Sam Derbyshire via John Baez. If you like algebra: these are plots of the density in the complex plane of roots of polynomials with small integral coefficients. If you don't: these are extravagantly beautiful images produced from the simplest of mathematical procedures. Explore the image interactively here.

## Chisenbop

Chisenbop - a tool for doing simple math on your fingers, invented by Sung Jin Pai in the '40s, it uses the same principles as the abacus. Tutorial 1 and 2, and a cute kid.

## Delightful Puzzles

A gathering of puzzles including many old chestnuts but also perhaps one or two you haven't met before.

## No fair! You got more than me!

## To Infinity Bagel, And Beyond!

"Center the bagel at the origin, circling the Z axis. A is the highest point above the +X axis. B is where the +Y axis enters the bagel. C is the lowest point below the -X axis. D is where the -Y axis exits the bagel."

## m(n,m)

Eminem's "Lose Yourself" re-envisioned as a high school math course. The math and film departments of Madison East High School collaborate on a video, starring math teacher Philip Galarowicz. Not to be confused with The Rappin' Mathematician (hear "The Number Line Dance" here), or these high school math rappers, or the rap battle of TI-83 and Fitty Slope. The quadratic formula, rapped. The quadratic formula, rapped again. The quadratic formula, rapped, strangely compellingly, by a teacher in a tie.

## Math education

How should math be taught? The Kumon Math curriculum provides a simple and clear description of one possible sequence of skills. Hung-Hsi Wu decries the bogus dichotomy of basic skills versus conceptual understanding (PDF, Google Docs). David Klein provides a detailed history of US K-12 math education in the 20th century. The NYT describes the 2008 report of the National Mathematics Advisory Panel (full text as PDF). [more inside]

## In Soviet Russia, equations solve you

## It Was a Monster Math!

## unbump.

## The crying of x^2 + xy + y^2 = 49

"Pynchon, postmodern author, is commonly said to have a non-linear narrative style. No one seems to have taken seriously the possibility, to be explored in this essay, that his narrative style might in fact be

*quadratic*." Number theorist Michael Harris on Pynchon and conic sections.## Math Overflow

Math Overflow is the first attempt to use the Stack Exchange platform, already popular with programmers, as a scientific research tool. Founded this month by a group of young mathematicians, including Scott Morrison and Ben Webster of the Secret Blogging Seminar, the site is already wrestling with hundreds of questions, ranging from the technical ("When is a map given by a word surjective?") to the historical ("Most interesting mathematics mistake?")

## Raise Thumb. Close One Eye. Squint.

The eyeballing game: compare your best attempts at several instinctive everyday tasks - determining a point of convergence, bisecting an angle, finding the midpoint of a line - against mathematical certainty. In a more financial mood? Play Chartgame: given a random historical stock chart of an unnamed S&P 500 company, choose to buy and sell as time advances to see if you can beat the market.

## Nate Silver accusess polling firm of fraud

42.7 percent of all statistics are made up: After Strategic Visions refused to share the methodology behind some of their polling, Nate Silver of fivethirtyeight analyzed the firm's poling results and found evidence of fraud. Strategic Visions responds to The Hill. More amusingly, Nate went on a look at an even more questionable study by the same company claiming that only 23 percent of Oklahoma students know that George Washington is the first president. [more inside]

## Math Geekery

For math geeks. How to Draw the Voronoi Diagram. Voronoi diagrams, as a geometric model are fascinating because they can be used to describe almost literally everything: from cell phone networks to radiolaria, at every scale: from quantum foam to cosmic foam. See also the Wallpaper Group: there are only 17 ways to fill a plane with a regular 2 dimensional pattern. Fred Scharmen [weblog home] is known as 765 and also produces a number of shapes, textures and patterns.

## More than just beautiful minds

Photographer Mariana Cook has a new book of portraits of well-known mathematicians. Here's a slideshow with some interesting audio, and more of the photographs.

## The P vs. NP problem and its importance

The Status of the P Versus NP Problem

*It's one of the fundamental mathematical problems of our time, and its importance grows with the rise of powerful computers.*(via mr)## Figure 3. Basic model outbreak scenario. Susceptibles are quickly eradicated and zombies take over, infecting everyone.

## Parkinson's Law

Why bureaucracy, like gas, fills up all available space. From the archive of

*The Economist*, 1955 [via ArchiveDigger.]## A constant reminder

"This day may be celebrated in a variety of ways. Pause and give thought to the role that the number pi has played in your life. Imagine a world without pi. Attempt to memorise pi to as many decimal places as you can. If you're feeling creative, devise alternative values for pi. Go to a party (I will). Or just celebrate in the time-honoured fashion of ignoring Pi Approximation Day altogether."

Happy Pi Approximation Day. [more inside]

Happy Pi Approximation Day. [more inside]

## I will choose free will

The Free Will Theorem - "If there exist experimenters with (some) free will, then elementary particles also have (some) free will." (previously)

## Gimme That Old Time Derivation

The Cornell Historical Math Monographs archive has a great many famous papers, including works by De Morgan, Hamilton, Descartes (warning: French) and of course Lewis Carroll. [more inside]

## I am a strange loop.

Douglas Hofstadter's

*Gödel, Escher, Bach: An Eternal Golden Braid*has been recorded as a series of video lectures for MIT's Open Courseware project.## Beware of Oddity

## Theory versus Statistics, Financial Economics Edition.

Theory versus Statistics, Financial Economics Edition. "You can almost here the lament of this quant that the real math theory has been dead since 1980, and that it has all been applied and statistics ever since. It’s like Fischer Black was Kool Herc and Myron Scholes was Afrika Bambaataa, and they’d all go plug in their computers into lamp posts and do martingale representations in the streets and at house parties. And, of course, it was all ruined in 1979 when it went commercial." A response to The Last Temptation of Risk by Barry Eichengreen.

## Computable data* (conceivably knowable) about people

Stephen Wolfram discusses Wolfram|Alpha: Computational Knowledge Engine - at the same time Google Adds Search to Public Data, viz: "Nobody really paid attention to the two hour snorecast" -- like a cross between designing for big data and a glossary of game theory terms -- on Wolfram|Alpha (previously), yet the veil is being lifted nonetheless: "[on] a platonic search engine, unearthing eternal truths that may never have been written down before," cf. hunch & cyc (and in other startup news...) [via] [more inside]

## The five states of Texas

Following the recent uproar over Texas and the possibility of its secession (previously), Fivethirtyeight.com puts forward a theoretical division of Texas into five states: Plainland, Trinity, Gulfland, New Texas, and El Norte.

## Information doesn't want to be scale free

"the scale-free network modeing paradigm is largely inconsistent with the engineered nature of the Internet..." For a decade it's been conventional wisdom that the Internet has a scale-free topology, in which the number of links emanating from a site obeys a power law. In other words, the Internet has a long tail; compared with a completely random network, its structure is dominated by a few very highly connected nodes, while the rest of the web consists of a gigantic list of sites attached to hardly anything. Among its other effects, this makes the web highly vulnerable to epidemics. The power law on the internet has inspired a vast array of research by computer scientists, mathematicians, and engineers.
According to an article in this month's Notices of the American Math Society, it's all wrong. How could so many scientists make this kind of mistake? Statistician Cosma Shalizi explains how people see power laws when they aren't there: "Abusing linear regression makes the baby Gauss cry."

## I want my MathTV

MathTV is a real problem solver for many. It is also found on YouTube, and is free. Here is some background.

## Dolphins caught on film making art and doing science.

Dolphins at SeaWorld Orlando make and play with bubble rings. Others learn by watching. (SLYP) via [more inside]

## The On-Line Encyclopedia of Integer Sequences

Ever wondered what comes next, and why? The On-Line Encyclopedia of Integer Sequences has the answers. (Previously.)

## MacTutor History of Mathematics archive

The MacTutor History of Mathematics archive is an astounding collection of historical material on mathematics, especially biographies. (Previously: 1 2 3 4.)

## A vote for "The Indefatigable Frog" is a vote for posterity.

"Do you like fiction and mathematics? Are you interested in what our society thinks about mathematicians?" [more inside]

## All Things Mathematical

Somewhere between 538 and xkcd, Ask Doctor Math is an advice column for practical math questions. [more inside]

## Welcome to the Khan Academy

Sal Khan likes explaining things, and he's really good at it. Here he is on CNN giving an excellent explanation of the financial crisis. And here's a great explanation of Newton's Law of Gravitation. His YouTube channel has over 700 lectures and you leave understanding everything he talks about no matter the subject.

## S_estina

The sestina is an old poetic form invented by the troubadors; each of the thirty-nine lines ends with one of only six words, which gives the sestina a haunting, constricted feel. You might have read modern examples by Bishop or Auden, or the even more modern "WTF Sestina" by Meghann Marco. But you have probably never read a sestina which explains how to construct a sestina in the language of finite group theory. (.pdf link) Via excellent mathblog God Plays Dice.

## Exponential, what it do?

Division: Work it out! - these girls be spittin the math.

## A beautiful truthful mind

Brain reorganizes to make room for math. But does math easily lead to truth? Is it really just beauty?

## Would you like to buy an fuzzy multi-instanton knot?

"...the best place to hide bulls**t is in a refereed journal that’s not open-access!" The math-physics blog n-category cafe digs into the curious case of M.S. El Naschie. El Naschie is editor-in-chief of the journal Chaos, Solitons, and Fractals, published by the well-respected scientific publisher Elsevier and sold to academic libraries for US$4,520 a year. The problem? El Naschie has published 322 of his own papers in the journal -- papers that John Baez (of "This Week's Finds in Mathematical Physics" and "The Crackpot Index") describes as "vague, dreamlike imagery," "undisciplined numerology larded with impressive buzzwords," and "total baloney." Is El Naschie a reverse Sokal? Or a Markov process for producing random publishable papers? One thing's for sure -- he knows how to cure cancer.

## Two mathematicians walk into a bar...

A math professor was explaining a particularly complicated calculus concept to his class when a frustrated pre-med student interrupts him. "Why do we have to learn this stuff?" the pre-med blurts out. The professor pauses, and answers matter-of-factly: "Because math saves lives." "How?" demanded the student. "How on Earth does calculus save lives?" "Because," replied the professor, "it keeps certain people out of medical school."

## What is the largest prime factor of the sum of the favorited comments from all fibonacci-numbered MeFites?

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."

Started in 2001 as a sub-section of Maths Challenge, it has since grown large enough to become its own entity. It now boasts over 200 problems, many of them insanely difficult. [more inside]

Started in 2001 as a sub-section of Maths Challenge, it has since grown large enough to become its own entity. It now boasts over 200 problems, many of them insanely difficult. [more inside]

## The Mathemagician and Pied Puzzler, and others

*The Mathemagician and Pied Puzzler*(PDF, rough table of contents here) is a collection of puzzles created by members of the Gathering 4 Gardner Foundation, in tribute to the man himself (previously). Also freely available at the G4G site is

*Puzzle Craft*(PDF), by Stewart Coffin. (

*The Puzzling World of Polyhedral Dissections*, also by Coffin, is available here.)