Simpsons Math

I just came across this awesome website dedicated to all the math trivia found in The Simpsons TV show.

P vs. NP

According to Vinay Deolalikar a research scientist at HP Labs, P is not equal to NP.

His preliminary manuscript can be found here.

Sorting Algorithms

My last post on sorting algorithms had static displays. This site shows animations for all the different sorts.

Sortvis

Sortvis is a sorting algorithm visualization project.

Click here for more information and to download the code.

XKCD Cartoon - 3x9

Tell Me A Joke

The Wolfram|Alpha search engine returns a different mathematical joke for a "Tell me a joke" query.

Martin Gardner: 1914-2010

Martin Gardner, a prolific writer and popularizer of mathematics, and one of the most influential figures in skepticism passed away on Saturday, May 22, 2010.

Click here for more information.

NIST Releases Successor to Venerable Handbook of Math Functions

The National Institute of Standards and Technology (NIST) has released the Digital Library of Mathematical Functions (DLMF) and its printed companion, the NIST Handbook of Mathematical Functions, the much-anticipated successors to the agency's most widely cited publication of all time. These reference works contain a comprehensive set of tools useful for specialists who work with mathematical modeling and computation.

Click here for more information.

No 'Simple Theory of Everything'

The "exceptionally simple theory of everything," proposed by a surfing physicist in 2007, does not hold water, says Emory mathematician Skip Garibaldi.

Garibaldi, a rock climber in his spare time, did the math to disprove the theory, which involves a mysterious structure known as E8. The resulting paper, co-authored by physicist Jacques Distler of the University of Texas, will appear in an upcoming issue of Communications in Mathematical Physics.

Click here for more information.

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Happy π Day!

Today is π Day. Google even changed their logo to promote that.

JSLab PlotTool

A graph plotting tool made entirely in JavaScript. It uses no graphics and the generated source code is W3C compliant.

Currently real valued functions of one variable and parameter functions for plane curves are supported. You can plot using a variety of options like line resolution and axis dimensions. The first beta also adds support for limited zoom functionality. As the graph is computed real time there is no limit for the zoom level.

MathJax

MathJax is an open source, Ajax-based math display solution designed with a goal of consolidating advances in many web technologies in a single definitive math-on-the-web platform supporting all major browsers.

Geeky Math Equation Creates Beautiful 3-D World

The quest by a group of math geeks to create a three-dimensional analogue for the mesmerizing Mandelbrot fractal has ended in success.

They call it the Mandelbulb. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.

Click here for more information.

Saturn’s Hexagon May Be Solar System’s Coolest Mystery

The Cassini spacecraft has returned the best images yet of the strange hexagonal jet stream that flows around the northern pole of Saturn.

First discovered by the Voyager spacecraft in the early 1980s, the hexagon remains a beautiful mystery to astronomers, and one they’ve been waiting for another shot to see for almost three decades.

Click here for more information.

Not So Fortunate Numbers

A Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m > 1 such that p_n# + m is a prime number, where the primorial p_n# is the product of the first n prime numbers.

For example, p₇# = 2×3×5×7×11×13 = 510,510. The smallest prime number after 510,511 is 510,529. Thus, 510,529 - 510,510 = 29 is a Fortunate number.

Fortune's conjecture states that no Fortunate number is composite. A Fortunate prime is a Fortunate number which is also a prime number. As of 2009, all the known Fortunate numbers are also Fortunate primes.

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Instead of only using primorial numbers in our sequence, what happens when we use all numbers such that for the largest prime dividing each number in our sequence, the primorial of that prime also divides that number (i.e., 630 = 2×3²×5×7 belongs to the sequence since p₄# = 210 divides 630)?

512 → 2⁵, 16,384 → 2⁹, and 524,288 → 2¹⁴ fail to generate Fortunate primes.

Do only perfect powers of two fail to generate Fortunate primes? Is there a pattern?

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For all numbers less than a billion in our sequence, the following fail to generate a Fortunate prime:

F#  Generator
9      512
9      8,388,608
15    4,194,304
15    67,108,864
21    524,288
25    147,456
25    373,248
25    393,216
25    1,062,882
25    1,259,712
25    4,251,528
25    4,718,592
25    5,308,416
25    5,971,968
25    10,077,696
25    17,915,904
25    21,233,664
25    35,831,808
25    42,467,328
25    172,186,884
27    16,384
35    1,119,744
35    1,492,992
35    33,554,432
35    47,775,744
35    150,994,944
35    362,797,056
49    22,118,400
49    31,104,000
49    32,805,000
49    42,187,500
49    56,623,104
49    90,000,000
49    286,654,464
49    364,500,000
49    720,000,000
49    859,963,392
55    679,477,248
65    10,616,832
77    159,252,480
77    188,956,800
85    322,486,272
119  314,572,800

J - An Amazing Programming Language

J is a modern, high-level, general-purpose, high-performance programming language. J is portable and runs on Windows, Unix, Mac, and PocketPC handhelds, both as a GUI and in a console.

Plouffe's Inverter

Simon Plouffe has a database of more than 215,000,000 mathematical constants like Pi, E, Catalan or Euler-Mascheroni constant with more than 2 billion digits.

Wolfram | Alpha

Check out the Wolfram|Alpha computational knowledge engine.

47th Known Mersenne Prime Found!

On April 12^th, the 47^th known Mersenne prime, 2^42,643,801-1, a 12,837,064 digit number was found by Odd Magnar Strindmo from Melhus, Norway! This prime is the second largest known prime number, a "mere" 141,125 digits smaller than the Mersenne prime found last August.

Click here for more information.

Best Visual Illusion of the Year Contest

The Best Visual illusion of the Year Contest is a celebration of the ingenuity and creativity of the world’s premier visual illusion research community. Contestants from all around the world have submitted novel visual illusions (unpublished, or published no earlier than 2008), and an international panel of judges has rated them and narrowed them to the TOP TEN.