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524 posts tagged with Math.

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524 posts tagged with Math.

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## Sure it's irrational! Just look!

Geometrically the irrationality of the square root of 2 means that there is no integer-by-integer square whose area is twice the area of another integer-by-integer square. A visual proof that the square root of 2 is irrational (not found in previous visual proof post.)

## My Prime Factorization Sweater

This is the sweater that proves that I am a Certified Math Nut.

## Why Netflix Never Implemented The Algorithm That Won The Netflix $1 Million Challenge

## Ice

## How to quantify all aspects of society

"Samuel Arbesman is a senior scholar at the Ewing Marion Kauffman Foundation and author of the forthcoming book 'The Half-Life of Facts'. His research and essays explore how to quantify all aspects of society." [more inside]

## The mathematical modelling of popular games by Nick Berry

H _ _ _ m _ n, Y a _ _ _ e e, _ _ t t _ _ _ h i p, _ h u t _ s & L a _ _ e r _ , R _ _ k , _ _ n d y _ _ _ _ , and _ _ r t s.

## A snack of classical mechanics

What is the Dzhanibekov effect? Known as the Tennis Racket theorem in English and documented by Vladimir Dzhanibekov in 1985 space, it is the result of unstable rotation about a principle axis.

## A Shory Biography of Emmy Noether

## Machines vast and sinister

We've discussed subblue/Tom Beddard and Mandlebulbs before, but two months ago L'Eclaireur Sévigné asked him to create a few animations for their 147-screen exhibition. And here are the hypnotic, terrifying results.

## Solve for Professor X

Pop Culture Math: Artist Matt Cowan breaks down pop-culture icons into basic formulas. [more inside]

## "As you can probably imagine, this took some effort to make."

"The calculator itself is just over 250x200x100 blocks. It contains 2 6-digit BCD number selectors, 2 BCD-to-binary decoders, 3 binary-to-BCD decoders, 6 BCD adders and subtractors, a 20 bit (output) multiplier, 10 bit divider, a memory bank and additional circuitry for the graphing function." Yes, someone built a working scientific calculator, in Minecraft.

## So that's why they call 'em fractals!

## WHAT TIME IS IT?!

Do you like Adventure Time? (previously) Do you like 8-Bit Game intros? Then you'll like the 8-bit Adventure Time Video Game Intro.

## The Angel Problem

## Newton and Leibniz invent calculus.

There were ways to find the tangent to a curve, and the area under one, in an ad hoc manner before the birth of calculus. It was even known that these two were inverses of each other.

## Number A Day

## Morpion Solitaire

Morpion Solitaire is a very simple pencil-and-paper, line-drawing game for which the best possible score is not known! New records are still being set.

## What is it like to have an understanding of very advanced mathematics?

What is it like to have an understanding of very advanced mathematics? A naive Quora question gets a remarkably long, thorough answer from an anonymous respondent. The answer cites, among many other things, Tim Gowers's influential essay "The Two Cultures of Mathematics," about the tension between problem-solving and theory-building. Related: Terry Tao asks "Does one have to be a genius to do maths?" (Spoiler: he says no.)

## Monte Carlo

Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF).-N. Metropolis

## Two PDFs about PDFs

An "Exciting Guide to Probability Distributions" from the University of Oxford: part 1, part 2. (Two links to PDFs)

## I put in a quadratic and all I got was this dumb parabola

Google will now graph! Google Post description.
Now... examples! sin(x), exp(x), x^2+2x+1. We're not nearly done... [more inside]

## Breaking the Coppersmith-Winograd barrier

*For twenty years, the fastest known algorithm to multiply two n-by-n matrices, due to Coppersmith and Winograd, took a leisurely O(n^2.376) steps. Last year, though, buried deep in his PhD thesis, Andy Stothers discussed an improvement to O(n^2.374) steps. And today, Virginia Vassilevska Williams of Berkeley and Stanford, released a breakthrough paper [pdf] that improves the matrix-multiplication time to a lightning-fast O(n^2.37*[more inside]

**3**) steps. [via]## Eleven Equations True Computer Science Geeks Should (at Least Pretend to) Know

## Putting a style in your crimp

*Le Crimp*(mostly

*en français*) is a French collective that explores organic and abstract geometric [ I | II | III ] (PDFs) approaches to the art of origami. Read the white papers, browse the gallery or watch videos of artworks being made or being used in still-motion animations

## Pythagasaurus

Pythagasaurus is the fabled Tyrannosaurus practiced in the skills of trigonometry and long division. Apparently he knows all eight numbers. [Via]

## That which does not kill us makes us stronger

`> comp.basilisk - Frequently Asked Questions ::`

Almost everything about the incident at the Cambridge IV supercomputer facility where Berryman conducted his last experiments has been suppressed and classified as highly undesirable knowledge. It's generally believed that Berryman and most of the facility staff died. Subsequently, copies of basilisk B-1 leaked out. This image is famously known as the Parrot for its shape when blurred enough to allow safe viewing. B-1 remains the favorite choice of urban terrorists who use aerosols and stencils to spray basilisk images on walls by night. But others were at work on Berryman's speculations...[more inside]

**Is it just an urban legend that the first basilisk destroyed its creator?**Almost everything about the incident at the Cambridge IV supercomputer facility where Berryman conducted his last experiments has been suppressed and classified as highly undesirable knowledge. It's generally believed that Berryman and most of the facility staff died. Subsequently, copies of basilisk B-1 leaked out. This image is famously known as the Parrot for its shape when blurred enough to allow safe viewing. B-1 remains the favorite choice of urban terrorists who use aerosols and stencils to spray basilisk images on walls by night. But others were at work on Berryman's speculations...

## Knotty Problems

Science through yarn: Wooly Thoughts. The Home of Mathematical Knitting, including knitted klein bottles and hyperbolic planes. The Museum of Scientifically Accurate Fabric Brain Art (previously). Much, much, more on knitting, crochet and quilting used to visualize complex theories in topology, probability, chaos and fractals. [more inside]

## Bach is easy. If she brings him up, you just smile and you say: “Ahh, Bach.”

Bach as graph. -- An interactive visualization of the Cello Suite No. 1, Prelude.

## "Try not to think too hard."

## Machines of Paper and Wood

Building a Computer 1: Numerals -

*recently my kids have been asking me about how computers work. I like to give in-depth answers to such questions, so we set out on a quest to understand how they work...*Follow-up parts 2 3 4 5 6 7 8 9 10 11 12 13 14 15.## Wheels within wheels

The best known packings of equal circles within a circle. Best packings with 1-12 circles. Best packings with 49-60 circles. Best packings with 1093-1104 circles. Also, circles whose areas form a harmonic series. Circles in an isosceles right triangle. Or generate your own circle packings. (Background for beginners: circle packing. Background for experts: circle packing.)

## Corporate fraud / Benford's law

One way to measure corporate fraud is look at reported numbers and see if they follow Benford's law - number sets that are manipulated usually deviate from Benford's law. A recent analysis of all public companies over the past 50 years has shown a steady upward deviation, strongly suggesting there is more corporate fraud now than ever before (peaked in 2008). [more inside]

## Jewish Problems

This is a special collection of problems that were given to select applicants during oral entrance exams to the math department of Moscow State University. These problems were designed to prevent Jews and other undesirables from getting a passing grade. (via Hacker News)

## Museum of Mathematics, NYC

## C is still for Cookie, and that's good enough for me

Science! (autoplaying video) The 42nd season of "Sesame Street," which premiered today, will be including a few new educational categories for preschoolers in its usual mix of lessons and parodies: STEM skills — Science, Technology, Engineering and Mathematics. In addition to more scientifically accurate slapstick, characters will try experiments, build bridges and boats, launch rockets and think through problems that require trial and error, observation and data -- all problem areas for America's students. [more inside]

## Who's afraid of the seven times table?

Who's Afraid of the Seven Times Table?

*Ernst Kummer, one of the great mathematicians of the late 1800s, was hopeless at arithmetic. He was giving an advanced maths lecture and in the middle of a complicated calculation he needed to know what six times seven was. “Um ... six times seven is ... six times seven . . .” A student put up his hand: “41, Professor.” Kummer chalked 41 on the blackboard. “No, no, Professor!” shouted another. “It’s 44!” Kummer gave the students a quizzical look. “Come, come, gentlemen. It can’t be both. It must be either one or the other!”*[more inside]## G.H. Hardy reviews Principia Mathematica

"Perhaps twenty or thirty people in England may be expected to read this book." G.H. Hardy's review of Whitehead and Russell's

*Principia Mathematica*, published in the Times Literary Supplement 100 years ago last week. "The time has passed when a philosopher can afford to be ignorant of mathematics, and a little perseverance will be well rewarded. It will be something to learn how many of the spectres that have haunted philosophers modern mathematics has finally laid to rest."## Math for Art Students

Systems, networks, and strategies is a math course being developed and taught this semester at the San Francisco Art Institute, by Lee Worden. The course-outline-in-progress is online at the linked wiki, including links to course materials like "the two-in-one-out game," "Places to intervene in a system," on-line flocking simulations, and "street math in graffiti art."

## Echoes Reality

## It does one thing and it does it well.

iTex2Img converts LaTeX equations into images online.

## Donald in Mathmagic Land

Donald in Mathmagic Land is a 27-minute Donald Duck featurette released on June 26, 1959. As Walt Disney said, "We have recently explained mathematics in a film and in that way excited public interest in this very important subject." (Wiki)

## Math interview podcast

Strongly Connected Components is a podcast of interviews with mathematicians. Hear complexity theorist Scott Aaronson (of Shtetl-Optimized), Tom Henderson (of Punk Mathematics) algebraist Olga Holtz of UC-Berkeley, master combinatorist Richard Stanley of MIT, and many more.

## The Earth Is Flat (to a certain approximation)

Old Theories As Limits of New Ones -- Theoretical physicist, Lubos Motl, takes a brief tour through the history of physics, and explains the simple mathematical relationship of old theories to the theories that replace them.

## Growing a hyperdodecahedron

This short computer graphics animation

*presents the regular 120-cell: a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron.*[more inside]## Lisa Sauermann is the world's best high school math competitor

Lisa Sauermann of Germany has won her fourth gold medal at the International Mathematical Olympiad, making her the top performer in the high school math competition's history. The IMO has been has been run continuously since 1959. Sauermann scored a perfect 42 on this year's exam, the only contestant in the world to do so. Not impressed yet? Here are this year's problems: day 1 and day 2. Watch a bunch of mathematicians wrestle with problem 2 in real time at the polymath blog.

## Kill Math

Bret Victor on WorryDream The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols.
When most people speak of Math, what they have in mind is more its mechanism than its essence. This "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots.

## Beaded Beads

Beaded Polyhedra ❂ More beadwork (mathematical and otherwise) by Gwen Fisher ❂ Still more beadwork galleries at beAdinfinitum ❂ Three-dimensional finite point groups and the symmetry of beaded beads [pdf - some algebra, but lots of illustrations]

## Then you wouldn't have to say "QED", 'cause I'd already know

A thread full of proofs without words at MathOverflow and quite a lot more of them courtesy of Google Books.

## Vermont 1, Rest of USA 0

## The Cartoon Guide to Life, the Universe, and Everything

Larry Gonick is a veteran American cartoonist best known for his delightful comic-book guides to science and history, many of which have previews online. Chief among them is his long-running

*Cartoon History of the Universe*(later*The Cartoon History of the Modern World*), a sprawling multi-volume opus documenting everything from the Big Bang to the Bush administration. Published over the course of three decades, it takes a truly global view -- its time-traveling Professor thoroughly explores not only familiar topics like Rome and World War II but the oft-neglected stories of Asia and Africa, blending caricature and myth with careful scholarship (cited by fun illustrated bibliographies) and tackling even the most obscure events with intelligence and wit. This savvy satire carried over to Gonick's Zinn-by-way-of-*Pogo*chronicle*The Cartoon History of the United States*, along with a bevy of*Cartoon Guides*to other topics, including*Genetics, Computer Science, Chemistry, Physics, Statistics, The Environment*, and (yes!)*Sex*. Gonick has also maintained a few sideprojects, such as a webcomic look at Chinese invention, assorted math comics (previously), the*Muse*magazine mainstay*Kokopelli & Co.*(featuring the shenanigans of his "New Muses"), and more. See also these lengthy interview snippets, linked previously. Want more? Amazon links to the complete oeuvre inside! [more inside]