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597 posts tagged with Math.

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## no stairway?

Q: How many miles is it to the crab nebula? How does one even figure this out?
A: The cosmic distance ladder! Here's a talk by Fields medalist Terrence Tao on methods for indirect calculation of distances to astronomical objects. Here's Tao's blog post on the subject, including the slides for the talk. And here's a Wikipedia page. [more inside]

## Boaler and the math wars

"Milgram and Bishop are opposed to reforms of mathematics teaching and support the continuation of a model in which students learn mathematics without engaging in realistic problems or discussing mathematical methods. They are, of course, entitled to this opinion, and there has been an ongoing, spirited academic debate about mathematics learning for a number of years. But Milgram and Bishop have gone beyond the bounds of reasoned discourse in a campaign to systematically suppress empirical evidence that contradicts their stance. Academic disagreement is an inevitable consequence of academic freedom, and I welcome it. However, responsible disagreement and academic bullying are not the same thing. Milgram and Bishop have engaged in a range of tactics to discredit me and damage my work which I have now decided to make public." Jo Boaler, professor of mathematics education at Stanford, accuses two mathematicians, one her colleague of Stanford, of unethical attempts to discredit her research, which supports "active engagement" with mathematics (aka "reform math") over the more traditional "practicing procedures" approach. [more inside]

## Smoothlife

SmoothLife is a continuous version of John Conway's Game of Life. When you tire of watching the hypnotic video you can read a technical description of SmoothLife on the arXiv. Then you can watch more videos of SmoothLife.

## weee eigenvectors

Eigenfaces for facial recognition. (

*This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces.*)## What is the smallest prime?

What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."

## Robert MacPherson interviewed

Robert MacPherson interviewed as part of the Simons Foundation's Science Lives series. MacPherson is among the founders of the modern theory of

*singularities*, points like a kink in a curve where the geometry of a space stops being smooth and starts behaving badly. In the interview, MacPherson talks about cultural differences between math and music, his frustration with high school math, growing up gay in the South and life as a gay man in the scientific community, smuggling $23,000 in cash into post-Soviet Russia to help mathematicians there keep the lights on, catastrophe theory, perverse sheaves, how to be a successful graduate student, stuttering, and of course the development of the intersection homology theory for which he is most well-known.## Making Math Fun

Is your elementary school youngster struggling with math? Are they a visual person? Would math games and videos help them learn? Enter Math Playground, to assist with problem solving and real world math. Try the enticing logic game Sugar, Sugar or beef up your math word problem skills. There are plenty of games to help educate while entertaining.

## I ♥ Cardioids

I ♥ Cardioids, Vi Hart's condensed awesome tackles parabolas, cardioids, circles and more. Related: Part 1 of Rolling Circles and Balls.

## While almost unknown to Americans, many Europeans have treasured these portraits

Cliff Stoll makes glass Klein bottles. He also sells imported portraits of Gauss.

## To Infinity and Somewhat Past That!

Are there as many odd numbers as there are all numbers? Can one infinity be bigger than another? TED Ed and Minute Physics both take a look at some of the mind boggling realities of Infinity.

## William Thurston

"The real satisfaction from mathematics is in learning from others and sharing with others." William Thurston, one of the greatest mathematicians of the 20th century, has died. He revolutionized topology and geometry, insisting always that geometric intuition and understanding played just as important a role in mathematical discovery as did the austere formalism championed by the school of Grothendieck. Thurston's views on the relation between mathematical understanding and formal proof are summed up in his essay "On Proof and Progress in Mathematics." [more inside]

## The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer’s Law

## bons mots, poems, math, knitting and logic

Entertaining, collected bon mots and surprisingly interesting, collected poems by various authors. From a likable math brainiac's site, Dr T.E. Forster, a Cambridge University lecturer. He also knits and writes about Buddhist logic [pdf]. Bonus, there's a fun gif.

## Fun with kinematics!

Racetrack is a game with very simple rules which nonetheless does a surprisingly good job of simulating the acceleration, braking, and handling of a race car. It can teach not only about inertia and kinematics, but also about optimal racing lines. Racetrack can be played with nothing more than a piece of graph paper and a pen, but there is also an online implementation called Vector Racer.

## "Your argument has to be beautiful."

Paul Lockhart, author of the famous Mathematician's Lament, has a new book coming out called Measurement, which tries to discuss mathematics "as an artful way of thinking and living". Lockhart discusses his passion for math and motives for writing the book in this video.

## Win with mathb.in!

"MathB.in is a website meant for sharing snippets of mathematical text with others on the web. This is a pastebin for mathematics… The post can be composed in a mixture of plain text, LaTeX and HTML."

## 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]

## Piaget Beer Gauge

The Piaget Beer Gauge - a product to clear up visual misunderstandings about height and volume in American bars.

## Why Johnny Can’t Add Without a Calculator

Slate: Technology is doing to math education what industrial agriculture did to food: making it efficient, monotonous, and low-quality. [more inside]

## The Art of π, φ and e

## Linear Programming Will Save Us From the Invisible Hand

As part of Crooked Timber's Seminar on Francis Spufford's work of speculative fiction "Red Plenty." Cosma Shalizi has posted "7800 words about optimal planning for a socialist economy and its intersection with computational complexity theory."

## Big (and small) Numbers

FatFonts creates numerical fonts where the amount of ink/pixels for each number is in direct proportion to its value.

## 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.)

## 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]