Posts Tagged ‘math’

Professor suspected of being a terrorist because of a math equation

May 11, 2016

Prof suspected of being a terrorist because of a #math equation http://usat.ly/273zpEI What if he’d drawn chemical models instead HT @Layth

http://www.usatoday.com/story/news/2016/05/07/professors-airplane-math-leads-flight-delay/84084914/

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Twisted Math and Beautiful Geometry » American Scientist

March 6, 2016

Twisted #Math & Beautiful Geometry
http://www.americanscientist.org/issues/id.16146,y.2014,no.2,content.true,page.1,css.print/issue.aspx nice overview of 4 tricky shapes: cycloids, epicycles, spirals & steiner prisms

A Group of American Teens Are Excelling at Advanced Math – The Atlantic

February 25, 2016

A Group of American Teens Are Excelling at…#Math
http://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/ To teach concepts or facts to the “educational 1-percenters”

Rock-paper-scissors may explain evolutionary ‘games’ in nature

September 8, 2015

Rock-paper-scissors may explain evolutionary ‘games’
http://news.sciencemag.org/biology/2015/05/rock-paper-scissors-may-explain-evolutionary-games-nature How aggressive, cooperative & deceptive behaviors can coexist

QT:{{”
“The hand game “rock-paper-scissors” is a classic way to settle playground disputes, with rock smashing scissors, scissors cutting paper, and paper covering rock. But it turns out that nature plays its own versions of the game, and mathematicians and biologists have used it to study everything from human societies to bacteria in a petri dish. Now, researchers have found that when players change their strategies on the fly, a stable pattern arises in which each of the three weapons gains and loses popularity in turn. The discovery could shed light on how living creatures maintain competing strategies in the struggle for existence.

When applied to biology, rock-paper-scissors blossoms from a two-person children’s game into a complex dance among multiple players. Certain lizards, for example, use three competing
strategies—aggression, cooperation, and deception—to win mates, with each tactic beating one and losing to another—just like rock, paper, and scissors. For the lizards, winning the game equates to making babies.

Inspired by computer simulations of a related game, two
mathematicians—Steven Strogatz and Danielle Toupo of Cornell University—decided to get to the root of what happens when players switch strategies midgame. “I thought it was fascinating, and I wanted to find a mathematical model that would describe this in its simplest form,” Strogatz says. They went back to basics, studying the pure equations instead of complicated computer simulations.”
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John Horton Conway: the world’s most charismatic mathematician | Siobhan Roberts | Science | The Guardian

September 4, 2015

John Horton Conway: the world’s most charismatic #mathematician
http://www.theguardian.com/science/2015/jul/23/john-horton-conway-the-most-charismatic-mathematician-in-the-world Floccinaucinihilipilification is his favourite word

Solving an Unsolvable Math Problem – The New Yorker

February 9, 2015

The pursuit of beauty http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty Zhang’s 2 accomplishments: Solving a #math mystery about gaps in primes & Doing it after age 50

Profiles FEBRUARY 2, 2015 ISSUE
The Pursuit of Beauty
Yitang Zhang solves a pure-math mystery
BY ALEC WILKINSON

Mathematicians Make a Major Discovery About Prime Numbers | WIRED

December 23, 2014

Major Discovery About #Prime Numbers
http://www.wired.com/2014/12/mathematicians-make-major-discovery-prime-numbers Extension of trick to find spans of composites, eg start w/ 101! add 2,3,4…101

QT:{{”
The two new proofs of Erdős’ conjecture are both based on a simple way to construct large prime gaps. A large prime gap is the same thing as a long list of non-prime, or “composite,” numbers between two prime numbers. Here’s one easy way to construct a list of, say, 100 composite numbers in a row: Start with the numbers 2, 3, 4, … , 101, and add to each of these the number 101 factorial (the product of the first 101 numbers, written 101!). The list then becomes 101! + 2, 101! + 3, 101! + 4, … , 101! + 101. Since 101! is divisible by all the numbers from 2 to 101, each of the numbers in the new list is composite: 101! + 2 is divisible by 2, 101! + 3 is divisible by 3, and so on. “All the proofs about large prime gaps use only slight variations on this high school construction,” said James Maynard of Oxford, who wrote the second of the two papers.
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Candy Crush’s Puzzling Mathematics » American Scientist

October 26, 2014

Candy Crush’s Puzzling #Mathematics http://www.americanscientist.org/issues/id.16278,y.2014,no.6,content.true,page.1,css.print/issue.aspx Game reducible to a NP-hard logic circuit; maybe useful in solving other problems

QT:{{"
To show that Candy Crush is a mathematically hard problem, we could
reduce to it from any problem in NP. To make life simple, my
colleagues and I started from the granddaddy of all problems in NP,
finding a solution to a logical formula. This is called the
satisfiability problem. You will have solved such a problem if you
ever tackled a logic puzzle. You have to decide which propositions to
make true, and which to make false, to satisfy some set of logical
formulae: The Englishman lives in the red house. The Spaniard owns the
dog. The Norwegian lives next to the blue house. Should the
proposition that the Spaniard owns the zebra be made true or false?

To reduce a logic puzzle to a Candy Crush problem, we exploit the
close connection between logic and electrical circuits. Any logical
formula can simply be represented with an electrical circuit.
Computers are, after all, just a large collection of logic gates—ANDs,
ORs, and NOTs—with wires connecting them together. So all we need to
do is show that you could build an electrical circuit in a Candy Crush
game.

The idea of problem reduction offers an intriguing possibility for
Candy Crush addicts. Perhaps we can profit from the millions of hours
humans spend solving Candy Crush problems? By exploiting the idea of a
problem reduction, we could conceal some practical computational
problems within these puzzles. Other computational problems benefit
from such interactions: Every time you prove to a website that you’re
a person and not a bot by solving a CAPTCHA (one of those ubiquitous
distorted images of a word or number that you have to type in) the
answer helps Google digitize old books and newspapers. Perhaps we
should put Candy Crush puzzles to similar good uses.

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A Billionaire Mathematician’s Life of Ferocious Curiosity

July 20, 2014

Billionaire Mathematician’s Life
http://www.nytimes.com/2014/07/08/science/a-billionaire-mathematicians-life-of-ferocious-curiosity.html “I wasn’t the fastest guy…but I like to ponder[;] turns out to be…pretty good.”

A Billionaire Mathematician’s Life of Ferocious Curiosity
http://www.nytimes.com/2014/07/08/science/a-billionaire-mathematicians-life-of-ferocious-curiosity.html

QT:{{
“I wasn’t the fastest guy in the world,” Dr. Simons said of his youthful math enthusiasms. “I wouldn’t have done well in an Olympiad or a math contest. But I like to ponder. And pondering things, just sort of thinking about it and thinking about it, turns out to be a pretty good approach.”
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Math Explains Likely Long Shots, Miracles and Winning the Lottery – Scientific American

April 12, 2014

#Math Explains Likely Long Shots: Nice illustration of the
combinatorics of why 23 people usually share a birthday
http://www.scientificamerican.com/article/math-explains-likely-long-shots-miracles-and-winning-the-lottery

http://www.scientificamerican.com/article/math-explains-likely-long-shots-miracles-and-winning-the-lottery/

QT:{{”

…because that’s the probability that none of them share my birthday, the probability that at least one of them has the same birthday as me is just 1 – 0.94. (This follows by reasoning that either someone has the same birthday as me or that no one has the same birthday as me, so the probabilities of these two events must add up to 1.) Now, 1 – 0.94 = 0.06. That’s very small.

Yet this is the wrong calculation to consider because that
probability–the probability that someone has the same birthday as you–is not what the question asked. It asked about the probability that any two people in the same room have the same birthday as each other. This includes the probability that one of the others has the same birthday as you, which is what I calculated above, but it also includes the probability that two or more of the other people share the same birthday, different from yours.

This is where the combinations kick in. Whereas there are only n – 1 people who might share the same birthday as you, there are a total of n × (n – 1)/2 pairs of people in the room. This number of pairs grows rapidly as n gets larger. When nequals 23, it’s 253, which is more than 10 times as large as n – 1 = 22. That is, if there are 23 people in the room, there are 253 possible pairs of people but only 22 pairs that include you.

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