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368 posts tagged with Mathematics.

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## noncommutative balls in boxes

Morton and Vicary on the Categorified Heisenberg Algebra - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]

## The Art of π, φ and e

## Unlearning Math

Learning and Unlearning Math explores topic in mathematics from the perspective of a teacher. The author has developed series of articles on such varied topics as Multiplication, Quantity,
Central Tendency, Math in Comics, and things not taught in schools. More recently, the blog has focused on the conventions for Mathematical Notation.

## "I asked myself,'Why can't it work?'"

16 year old student from Germany solves 350 year old Isaac Newton puzzle Shourryya Ray, a 16-year-old German student, has cracked a puzzle that has stumped mathematicians since Sir Isaac Newton first posed the problem more than 350 years ago.
The teen's solutions allow exact calculations of a trajectory under gravity and subject to air resistance.
Bonus video of Neil Degrasse Tyson talking about Newton.

## Because Print Is Not Yet Dead

Free online graph paper generators: variations of squares, triangle, rhombus, and hexagonal, circular and polar, for drawing, gaming, writing, note-taking and much more. Blank Sheet Music (Flash) for all arrangements (PDF). Create and edit your own grids, probability and logarithmic graphs, petri-dish inserts and storyboards. Also, multilingual monthly and yearly calendars. Plus, more than you ever wanted to know about ISO paper dimensions and printable paper models of polyhedra. Prev-ious-ly.

## One Big Mac plus another Big Mac....

That the conventional wisdom of 3,500 calories less is what it takes to lose a pound of weight is wrong. The body changes as you lose. Interestingly, we also found that the fatter you get, the easier it is to gain weight. An extra 10 calories a day puts more weight onto an obese person than on a thinner one. [more inside]

## Cool Math Conundrums

In Russian roulette, is it best to go first? | The Mathematics of Tetris | What is the result of infinity minus infinity? [more inside]

## 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.)

## The Strangest Man

*The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject, a method which has not yet been applied successfully, but which I feel confident will prove its value in the future. The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty.*[1939] [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 Shory Biography of Emmy Noether

## Still plenty of room for improvement

"He is the kind of boy who is bound to be rather a problem in any school or community, being in some respects definitely anti-social." Alan Turing's school reports.

## The Hacker Shelf

The Hacker Shelf is nice crowd-sourced guide to (legally) free books on various computational and mathematical subjects. The topics page gives you an idea of the breadth of material available.

## You Complete Me

What is the minimal number of clues necessary to create a uniquely solvable Sudoku puzzle? It turns out to be 17, though it took fancy symmetry arguments and nearly a year of computer time to prove it. But no need to read the paper when you can watch the video.

## My best known work is in game theory

## Pineapple under the sea.... Really?

*So, Nickelodeon, you tell us that Spongebob Squarepants lives in a pineapple upside down house at the bottom of the sea. Are you really sure about that? Beware of misleading your viewers about the universe, Nickelodeon!*[more inside]

## garden of quasiperiodic rhombus tilings

Need some quasiperiodic tilings? Alan Schoen has a smorgasbord of tilings of rhombuses with pentagonal, heptagonal, and nonagonal symmetry that come in many flavors. Be sure to check out his page on triply periodic minimal surfaces and the other curios at his Geometry Garret.

## Mathematics and the Great Pyramid

*This is a radical statement about the Pyramid, especially on the internet because all web pages that I have been able to find that deal with the Pyramid, maintain that it was built and/or inspired by either God or space aliens. Most don't even consider that it could be a rational structure designed and built by normal people.*

## 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)

## Applied Ultrafinitism OR Amending a Forgotten Parameter

S. Ekhad , E. Georgiadis, D. Zeilberger.

*"How to Gamble If You're In a Hurry."*arXiv:1112.1645v1 (pdf), 7 Dec 2011. [more inside]## 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

## 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]

## 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

## Creating the Future of Education and Work

In February 2011, every teacher in Providence, Rhode Island was pink slipped. Not all 1,926 of them got fired, of course, but with the district facing a $40 million deficit, anything is possible. The district says it needs flexibility, just in case. Every school district in the United States faces its own version of what’s happening in Providence. However, “IMAGINATION: Creating the Future of Education and Work” is focused not on how we got here but rather how we can move forward from here immediately even as the education system continues to struggle. [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."## The mathematical sculptures of Henry Segerman

Henry Segerman creates mathematical sculptures using 3D printing:
Round Möbius Strip,
Hopf Fibration,
Half of a 120-cell,
Rectified Tesseract,
Tesseract and 16-cell,
Hilbert Curve,
Knotted Cogs,
Round Klein Bottle [more inside]

## I have a burning question, man.

*Before it was a website, Ask A Mathematician / Ask A Physicist was two guys sitting in the desert at Burning Man, presuming to answer (almost) any question that happened to occur to whomever happened to appear at our stand.*[more inside]

## What is up with Noises? (SLYT)

What is up with Noises? A fascinating explanation of why we hear sounds and music the way we do. It's a long video, but it's worth it!

## 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.

## Technically elegant but nearly forgotten

Ron Doerfler's Dead Reckonings - Lost Art in the Mathematical Sciences is a collection of essays, in weblog format, on historical techniques in mathematical sciences, antique scientific instruments and other related topics. [more inside]

## 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]

## i + e = δ

144 sites for online education. Categories include science and health, business and money, history and culture, law, computer science, mathematics, and languages. [more inside]

## 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.

## Transcendental Music

Happy Tau Day! τ (2 × π, that is, 6.28...) is the number of radians in a turn. Translating the digits to notes even makes beautiful music. (By comparison, what pi sounds like). Previously.

## What is the title of this post?

92 years young, the delightful Raymond Smullyan is a mathematician, logician, magician, concert pianist, and Taoist philosopher - who also pioneered retrograde chess problems.

## Microsoft Mathematics CAS

Microsoft Mathematics is a free Computer Algebra System (CAS) available from Microsoft. A CAS is a program that can solve purely symbolic mathematical equations. For example, the program can tell you that the derivative of 6x^2 + 12x is 12x + 12. The program has functions for calculus, statistics, linear algebra, and graphing. One interesting feature of the program is that in some cases it can show and describe the intermediate steps involved in solving an equation. Here’s a 16 page tutorial (in MS Word docx format) showing how to use the program. The program can be downloaded from the Microsoft download page. Thirty-two and sixty-four bit versions are available. The program only works on XP/Vista/Windows 7.

## Is teacher evaluation statistical voodoo?

"Value-added modeling is promoted because it has the right pedigree -- because it is based on "sophisticated mathematics." As a consequence, mathematics that ought to be used to illuminate ends up being used to intimidate." John Ewing, president of Math for America and former executive director of the American Mathematical Society, criticizes the "value-added modeling" approach used as a proxy for teacher quality, most famously in a Los Angeles Times story that called out low-scoring teachers by name. A Brookings Institution paper says value-added modeling is flawed but the best measure we have of teacher value, arguing that the metric's wide fluctuations from year to year are no worse than those of batting averages in baseball. (Though the weakness of that correlation is mostly a BABIP issue.) Can we assign a numerical value to teacher quality? If so, how?

## Not a cryptic FPP

Vortex-based mathematics is the most advanced ever known to mankind. Don't have time for a time cube? Time need no longer limit us. Here, Marco Rodin (inventor of the Rodin Coil) gives us the background.

## Nature Special Issue on the Future of the PhD

## Villians spotted at Melbourne University!

The annual Melbourne University Puzzle Hunt is back - and this time they need your help fending off villians with your puzzle-solving abilities. Anyone from anywhere in the world can compete in teams of 1 to 10 people (or you can see the puzzles for yourself and play at home). [more inside]

## Dear NASA, Your Mom thought I was big enough. Love, Pluto

Following in the footsteps of prestigious publications like the Annals of Improbable Research, NCBI ROFL, Rejecta Mathematica, the Journal of Universal Rejection, and the Journal of Unpublished Results, comes the Journal of Are You Fucking Kidding. Previous, previously, and previouslier.
h/t to Retraction Watch

## J programming language

The J programming language is kind of like a super calculator (it’s been described as executable mathematical notation). It was developed by Ken Iverson and Roger Hui and is a successor to APL (and there’s no need to buy a new keyboard). The language is free and open source, and works on Windows, Mac, and Linux. A series of books and articles on using J are also available to download. To whet your appetite, here’s an article on using J to find the eighth ten-digit prime number that appears among the digits of pi.

## MathML and LaTeX users rejoice

"MathJax is an open source JavaScript display engine for mathematics that works in all modern browsers." Displaying math and equations in web pages has been a pretty consistent problem. MathJax allows you to use either MathML or TeX/LaTeX as input and then formats it into beautiful, scalable HTML.

## pi-winning

## Talking fast and making cool videos does not mean learning is happening

So you're me and you're in math class and you're learning about graph theory, a subject too interesting to be included in most grade school's curricula so maybe you're in some special program or maybe you're in college and were somehow not scarred for life by your grade school math teachers. [more inside]

## Finite formula found for partition numbers

New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]

## Explorations of a Recreational Mathematician

Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]