Mathematically Related

Solar System Explained From the Inside Out

2011-12-06T18:11:00.001-05:00

An excellent image showing the scale of our solar system.

Japanese man calculates pi to 10 trillion digits

2011-10-20T06:58:00.000-04:00

The latest number-crunching champ isn't a supercomputer--it's a hacked-together PC.

Shigeru Kondo of Iida, Nagano Prefecture, worked with software designed by Northwestern University grad student Alexander Yee, and followed up their 2010 feat of reckoning pi to 5 trillion digits.

The result was achieved earlier this month after 371 days of computation and numerous hard drive failures.

Click here for more information.

Babbage Analytical Engine designs to be digitised

2011-09-21T11:55:00.000-04:00

A project to construct one of the earliest mechanical computers based on sketches by its designer, Charles Babbage, has received a major boost.

The Science Museum in London has agreed to help by digitising the mathematician's original plans.

Eventually the images will be used to create a full working model of the Analytical Engine.

Click here for the full article.

Crazy Japanese Math

2011-08-03T20:32:00.001-04:00

This is one way to keep kids (i.e., boys) interested in math. Too bad I can't read it.

Economy Statistics

2011-08-03T20:26:00.003-04:00

Due to the ongoing bad economy, I decided to add a couple of statistical graphs to show that.

U.S. National Debt Clock : Real Time

US debt problem visualized: Debt stacked in 100 dollar bills

The Batman Equation

2011-08-03T20:21:00.005-04:00

FRACTRAN

2011-05-24T20:04:00.003-04:00

I came across this mathematical programming article on Wikipedia called FRACTRAN.

FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway.

What an amazing methodology. I decided to buy the referenced book "Nonplussed!: Mathematical Proof of Implausible Ideas". It's easy to read, but the proof is still difficult to follow. I really need to read it again.

π = 4!

2011-03-15T06:44:00.003-04:00

Extended Midy's Theorem

2011-02-06T15:03:00.004-05:00

This is my proof, and an extension, of Midy's Theorem. Someone had referenced this in Wikipedia almost six years ago, but it was recently removed (still in the history) to make Wikipedia more official. Since this blog came about after my proof, I never went back and added it.

Microsoft Mathematics 4.01

2011-01-18T10:16:00.001-05:00

Microsoft Mathematics provides a graphing calculator that plots in 2D and 3D, step-by-step equation solving, and useful tools to help students with math and science studies.

Be sure to download the Microsoft Mathematics Add-In for Word and OneNote as well.

Scale Of The Universe

2010-12-21T21:17:00.002-05:00

Great flash website that shows the scale of the universe.

Vi Hart

2010-12-17T09:16:00.002-05:00

An interesting article on Vi Hart.

Also check out her blog for more cool, math videos.

NetCalc

2010-11-17T06:26:00.000-05:00

NetCalc.org is a prototype web-based graphic calculator aiming to provide advanced mathematical functionality. Functions can be viewed graphically, in table form and as a summary of area and mean values.

Benoît Mandelbrot, Novel Mathematician, Dies at 85

2010-10-16T22:06:00.001-04:00

Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.

Click here for more information.

Check out Skytopia's website for 3D Mandelbrot fractals.

Simpsons Math

2010-08-25T09:19:00.002-04:00

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

P vs. NP

2010-08-09T06:26:00.002-04:00

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

2010-07-13T11:52:00.002-04:00

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

Sortvis

2010-07-13T11:40:00.004-04:00

Sortvis is a sorting algorithm visualization project.

Click here for more information and to download the code.

XKCD Cartoon - 3x9

2010-07-08T07:14:00.003-04:00

Tell Me A Joke

2010-05-27T06:20:00.003-04:00

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

Martin Gardner: 1914-2010

2010-05-25T13:56:00.002-04:00

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

2010-05-19T13:03:00.001-04:00

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'

2010-05-19T12:59:00.002-04:00

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.

Click here for original post.

Happy π Day!

2010-03-14T09:08:00.002-04:00

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

JSLab PlotTool

2010-02-11T11:30:00.002-05:00

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

2009-12-17T06:55:00.001-05:00

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

2009-12-11T07:58:00.004-05:00

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

2009-12-11T07:55:00.002-05:00

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

2009-11-05T08:32:00.022-05:00

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

2009-07-28T21:55:00.001-04:00

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

2009-07-28T21:54:00.000-04:00

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

2009-07-28T21:52:00.002-04:00

Check out the Wolfram|Alpha computational knowledge engine.

47th Known Mersenne Prime Found!

2009-06-15T06:36:00.005-04:00

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

2009-06-03T08:57:00.001-04:00

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.

Free Mathematics Books

2009-03-29T22:01:00.000-04:00

Found this website with links for free mathematical e-books.

Quite Basic -- Sieve of Eratosthenes

2009-02-28T11:57:00.001-05:00

A BASIC programming website that uses the Sieve of Eratosthenes as an example.

Gallery of Illustrations

2009-02-28T11:55:00.000-05:00

An interesting website that has plenty of mathematical illustrations.

Number Puzzles

2009-02-24T14:35:00.004-05:00

Found some great number puzzles on the Internet.

Bridges
Dominosa
Light-up
Loop
Nonograms
Nurikabe
Shikaku
Sudoku

Drunk Men Work Here

2009-01-25T08:35:00.002-05:00

This is a very interesting website. Problems 170 and 129 are a couple of great logic games.

Security Codes

2009-01-05T13:46:00.021-05:00

I was entering the four-digit security code to our house, and I realized that it doesn't end with an ENTER (E) key to accept it. The problem with that is you can keep pressing numbers until the right combination is found. Since most keypads use all ten digits (0-9), the total number of combinations should be $10^n$. However, it is the ENTER key that makes it so difficult.

Let D equal the number of digits for the security code. Let K equal the number of digits on the keypad.

For a binary keypad (0, 1) and a three-digit code, our set consists of (000E, 001E, 010E, 011E, 100E, 101E, 110E, 111E). Thus, we have at most $2^3 \times (3+1)$ possible keys to enter, where the plus one is for the ENTER key. Generally speaking, we'd have $K^D \times (D+1)$ possible keys to enter.

Without the ENTER key, we could keep pressing the keypad until all combinations have formed. The minimum number of keys required would be $K^D + D$.

So for a binary keypad, we'd have:

D	String	Keys (wo/ E)	Keys (w/ E)
1	01	2	4
2	00110	5	12
3	0001110100	10	32
4	0000111100101101000	19	80
5	000001111100010010101110110011010000	36	192

Thus, one only needs to know the string concatenations to be able to guess the right combination if no ENTER or code-stopper key is required.

Update: See De Bruijn Sequence and ProjectEuler #265 for a related problem.

Cinderella

2008-12-16T11:03:00.000-05:00

Experience Geometry on your desktop and on the web. Easily create startling geometric constructions! Starting from simple triangle relations, continuing with trigonometric theorems up to fractals and transformation groups Cinderella lets you create and manipulate visualizations in an intuitive, yet powerful way.

Click here for more information.

Wolfram Mathematica Online Integrator

2008-12-01T15:23:00.000-05:00

This online integrator from Wolfram is actually pretty cool.

Worldmapper

2008-11-14T13:44:00.000-05:00

Worldmapper is a collection of world maps, where territories are re-sized on each map according to the subject of interest.

How online games are solving uncomputable problems

2008-11-10T08:59:00.000-05:00

Online games that tap your brainpower without you noticing can crack problems that have defeated the most powerful computers, says Lewis Dartnell. Get involved with distributed computing with these online games and downloads.

Click here for more information.

The Eyeballing Game

2008-10-06T11:12:00.002-04:00

The Eyeball website gives you some mathematical figures and asks you to eyeball them correctly. I scored a 5.92 on my first try.

Just scored 3.13 on my second try.

More games at the Games for the Brain website.

Titanic Primes Raced to Win \$100,000 Research Award

2008-09-16T10:43:00.005-04:00

Researchers have discovered the two largest known prime numbers, a whopping 12,978,189 and 11,185,272 digits long, as part of a 12 year old, world-wide volunteer computing project, the Great Internet Mersenne Prime Search ("GIMPS"). The primes can be written shorthand as $2^{43,112,609}-1$ and $2^{37,156,667}-1$. The larger number qualifies for a \$100,000 research award, most of which GIMPS will donate to the University of California, Los Angeles (UCLA), and to charity.

Click here for more information.

F#

2008-08-29T13:34:00.000-04:00

I'm learning F#, Microsoft's latest functional programming language for the .NET family. Very nice and interesting. I recommend buying these books on it: F# for Scientists, Foundations of F#, and Expert F#.

Proof of the Existence of God

2008-07-31T08:28:00.000-04:00

Click here for the explanation.

Lucy Pringle's Crop Circle Photograph Library

2008-06-19T22:13:00.000-04:00

Latest crop circle found in England. Original article here.

XKCD Cartoon - Purity

2008-06-11T10:35:00.001-04:00

WorldWide Telescope

2008-05-13T19:01:00.000-04:00

The WorldWide Telescope (WWT) is a Web 2.0 visualization software environment that enables your computer to function as a virtual telescope—bringing together imagery from the best ground and space-based telescopes in the world for a seamless exploration of the universe.

Processing

2008-05-09T13:15:00.000-04:00

Processing is an open source programming language and environment for people who want to program images, animation, and interactions. It is used by students, artists, designers, researchers, and hobbyists for learning, prototyping, and production. It is created to teach fundamentals of computer programming within a visual context and to serve as a software sketchbook and professional production tool. Processing is developed by artists and designers as an alternative to proprietary software tools in the same domain.

There's also a Javascript version of the code.

OpenVisuals

2008-05-09T13:06:00.000-04:00

OpenVisual is a visualization that is created using Processing and OpenVisuals API, which makes it possible to use with any datasets on this website. Visualization artists can use these datasets to build a visualization. Once they upload the visualization to this website, it can also be used to visualize any other dataset on this website through OpenVisuals API.

Glimpses Of A New Mathematical World

2008-04-15T13:53:00.000-04:00

A new mathematical object was revealed yesterday during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics.

Click here for more information.

Building a 5-ton mechanical calculator... from 19th-century plans

2008-04-15T10:00:00.000-04:00

Starting in May, many will have the opportunity to see for themselves how they did computing the old-fashioned way: with lots of gears, a big crank and some muscle.

The Computer History Museum, in Mountain View, Calif., will unveil a new construction, the first in the United States, of the 19th century British mathematician Charles Babbage’s Difference Engine No. 2, an improved version of his earlier mechanical digital calculator.

Click here for more information.

Rubik’s Cube Proof Cut to 25 Moves

2008-03-27T10:58:00.001-04:00

Last year, a couple of fellas at Northeastern University with a bit of spare time on their hands proved that any configuration of a Rubik’s cube could be solved in a maximum of 26 moves.

Now Tomas Rokicki, a Stanford-trained mathematician, has gone one better. He’s shown that there are no configurations that can be solved in 26 moves, thereby lowering the limit to 25.

Full article here.

Pi Day

2008-03-14T22:58:00.000-04:00

Happy Pi Day (3/14).

Slabacus (Slide Rule & Abacus Simulator)

2008-03-13T12:49:00.000-04:00

The slide rule & abacus simulators teach you how to use these two tools.

The Sheet-Based Calculator (Part II)

2008-02-25T14:53:00.000-05:00

After finding the Sheet-Based Calculator link and source code, I decided to download it and improve it for my Java learning experience and also because it's neat. :-)

Here's a link to the JAR file if you're interested.

Geometry Constructions->LaTeX Converter (GCLC)

2008-02-20T10:13:00.000-05:00

GCLC (from "Geometry Constructions->LaTeX converter") is a tool for visualizing and teaching geometry, and for producing mathematical illustrations. Its basic purpose is converting descriptions of mathematical objects (written in the GCL language) into digital figures. GCLC provides easy-to-use support for many geometrical constructions, isometric transformations, conics, and parametric curves. The basic idea behind GCLC is that constructions are formal procedures, rather than drawings. Thus, in GCLC, producing mathematical illustrations is based on "describing figures" rather than of "drawing figures".

The Sheet-Based Calculator

2008-02-20T10:12:00.000-05:00

The Sheet-Based Calculator allows you to enter normal mathematical expressions in a word-processor-like environment, but then to execute them as well. Its algorithm is implemented by using compiler concepts and parser grammar rules. It can be used in most operating systems because it is written in Java.

Visual Mathematics Dictionary

2008-02-08T09:32:00.000-05:00

An interesting site with plenty of visual definitions for all school grades.

History's Greatest Gadgets

2008-02-04T11:32:00.000-05:00

It's not all about circuits, silicon and stock options: mankind's been making technology since the dawn of time. Here is ten of the most wonderful gadgets from centuries—and millenia—past.

Running the Numbers

2008-01-24T10:28:00.000-05:00

An interesting set of pictures by Chris Jordan that shows the sizes of various U.S. consumptions.

New Smartpen And Paper To Help Teach Blind College Students

2008-01-18T22:30:00.000-05:00

A new smartpen and paper technology that works with touch and records classroom audio aims to bring these subjects to life for blind students.

The History of the Earth in a Toilet Paper Roll

2008-01-16T13:36:00.000-05:00

The earth is over 5 billion years old. Life first originated in the oceans 3.4 billion years ago. The dinosaurs died out 65 million years in the past. Human recorded history stretches back 10,000 years in time.

These numbers are too large to visualize, and difficult to compare. Here's an easy way to put time in perspective, and actually visualize different eras in the earth's history. You'll need a roll of toilet paper, a long hallway, and some sticky notes.

Click here for more information.

Statistics Calculators

2008-01-14T21:08:00.000-05:00

These statistics calculators are free to be used by anyone in the research community at large.

Notable Properties of Specific Numbers

2008-01-14T11:24:00.001-05:00

An interesting website for certain numbers.

Art Exhibit Features RFID Math Problems

2008-01-08T10:13:00.000-05:00

There's an awesome exhibit right now at the Mori Art Museum titled "Roppongi Crossing 2007: Future Beats in Japanese Art." It introduces some of the most important classic futurist artists from Japan as well as up-and-coming ones.

Pictured here is Math Gates. Designed by two professors—one math prof from Kyoto University and one new media expert from Tokyo National University—it's an interactive installation in which visitors carry RFID cards with math problems on them. The goal is to reach a pre-determined number—kinda like in the license plate number game. The idea behind it is to gain a better understanding of a computer's logic circuits. After all, humans aren't that different from machines, and machines are made by humans.

The exhibit runs through Jan 14, 2008.

Click here for original link.

Secret Websites, Coded Messages: The New World of Immersive Games

2008-01-01T21:20:00.000-05:00

Interesting story on how the music group Nine Inch Nails encoded a few hidden messages in one of their tours and albums.

To play it on the Wired site, select all text in each section (two sections) up to the input boxes of that section (or do the entire page at once) and paste it into Microsoft Word. Remove all formatting that has Font Color equal to Automatic and only the colored text remains. What the sentences mean and which ones to use, with punctuation, should become obvious.

'Mathlete' Smashes Human Calculation Record

2007-12-13T10:47:00.000-05:00

The world's fastest human calculator on Tuesday broke his own record for working out a 200-digit number using nothing but brain power to produce the answer in just over 70 seconds.

Alexis Lemaire, a 27-year-old Frenchman, correctly calculated the 13th root of a random 200-digit number from a possible 393 trillion answers.

Click here for more information.

Voyager 2 Probe Reaches Solar System Boundary

2007-12-11T09:18:00.000-05:00

The Voyager 2 spacecraft has crossed an important space frontier called the termination shock, and in a few years may become the first object made by humans to travel outside the solar system.

Click here for more information.

VisIt

2007-12-10T19:22:00.000-05:00

VisIt is a free interactive parallel visualization and graphical analysis tool for viewing scientific data on Unix and PC platforms. Users can quickly generate visualizations from their data, animate them through time, manipulate them, and save the resulting images for presentations. VisIt contains a rich set of visualization features so that you can view your data in a variety of ways. It can be used to visualize scalar and vector fields defined on two- and three-dimensional (2D and 3D) structured and unstructured meshes. VisIt was designed to handle very large data set sizes in the terascale range and yet can also handle small data sets in the kilobyte range.

Polyhedra.org

2007-12-07T11:28:00.000-05:00

Polyhedra.org is a collection of interactive models based on the canvas element.

The Universal Digital Library

2007-12-06T09:50:00.000-05:00

The mission is to create a Universal Library which will foster creativity and free access to all human knowledge. As a first step in realizing this mission, it is proposed to create the Universal Library with a free-to-read, searchable collection of one million books, available to everyone over the Internet. Within 10 years, it is our expectation that the collection will grow to 10 Million books. The result will be a unique resource accessible to anyone in the world 24×7, without regard to nationality or socioeconomic background.

Also see my previous post on the World Digital Library.

Sliding Block Puzzles

2007-12-02T18:03:00.000-05:00

Very challenging sliding-block puzzles at PuzzleBeast.

A Visual Dictionary of Special Plane Curves

2007-12-02T18:01:00.000-05:00

The name says it all. Also check out the main page.

The Descartes Circle Theorem

2007-12-01T20:20:00.000-05:00

When Kissing Involves Trigonometry is a very interesting article on the Descartes Circle Theorem.

Crayon Physics Deluxe

2007-12-01T20:17:00.000-05:00

Crayon Physics Deluxe is a sequel to the popular freeware game Crayon Physics. Or you can think of it as the game I would have created if I would have had more than 7 days to do it. Way more than 7 days. More like 7 months or 17 months.

Anyway Crayon Physics Deluxe is a 2D physics puzzle game, in which you get to experience what it would be like if your drawings would be magically transformed into real physical objects. Solve puzzles with your artistic vision and creative use of physics.

Möbius Transformations Revealed

2007-11-27T09:12:00.000-05:00

Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity. It was one of the winners in the 2007 Science and Visualization Challenge and was featured along with the other winning entries in the September 28, 2007 issue of journal Science.

Surfer dude stuns physicists with theory of everything

2007-11-15T16:32:00.000-05:00

An impoverished surfer has drawn up a new theory of the universe, seen by some as the Holy Grail of physics, which has received rave reviews from scientists.

Click here for more information.

His paper can be downloaded here.

A previous article can be found here.

Dataplot

2007-10-28T21:27:00.000-04:00

Dataplot is a free, public-domain, multi-platform (Unix, VMS, Linux, Windows 95/98/ME/XP/NT/2000, etc.) software system for scientific visualization, statistical analysis, and non-linear modeling. The target Dataplot user is the researcher and analyst engaged in the characterization, modeling, visualization, analysis, monitoring, and optimization of scientific and engineering processes.

SpeedCrunch

2007-10-28T21:21:00.000-04:00

SpeedCrunch is a fast, high precision and powerful desktop calculator.
Available for Linux, Microsoft Windows, and Mac OS X.

The Simplest Universal Turing Machine Is Proved

2007-10-24T13:04:00.000-04:00

Stephen Wolfram comments on the simplest universal Turing machine found.

See my previous blog as well.

For those of us that this is over our heads, buy his book, A New Kind of Science, for further explanation (which I hope to do soon).

Islamic Star Patterns

2007-10-19T11:20:00.000-04:00

Islamic star patterns arose in the centuries after the birth of Islam, and spread quickly as Islamic rule grew outward from the Middle East to encompass western Europe, northern Africa, and southern Asia. This form of ornamentation peaked in the first half of the second millennium. The practice then tapered off as the borders of the Muslim world began to shrink. Today, historical artifacts can be found in countries from Spain to Uzbekistan, with important concentrations in Spain, Turkey, Iran, and Morocco.

Click here for more information.

World Digital Library

2007-10-18T10:18:00.000-04:00

The World Digital Library will make available on the Internet, free of charge and in multilingual format, significant primary materials from cultures around the world, including manuscripts, maps, rare books, musical scores, recordings, films, prints, photographs, architectural drawings, and other significant cultural materials. The objectives of the World Digital Library are to promote international and inter-cultural understanding and awareness, provide resources to educators, expand non-English and non-Western content on the Internet, and to contribute to scholarly research.

Brain Man

2007-10-12T21:10:00.000-04:00

Almost 25 years ago, 60 Minutes introduced viewers to George Finn, whose talent was immortalized in the movie "Rain Man." George has a condition known as savant syndrome, a mysterious disorder of the brain where someone has a spectacular skill, even genius, in a mind that is otherwise extremely limited.

Morley Safer met another savant, Daniel Tammet, who is called "Brain Man" in Britain. But unlike most savants, he has no obvious mental disability, and most important to scientists, he can describe his own thought process. He may very well be a scientific Rosetta stone, a key to understanding the brain.

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Optical Illusions and Visual Phenomena

2007-10-12T13:06:00.000-04:00

This site demonstrates visual phenomena, and optical or visual illusions. The latter is more appropriate, because most effects have their basis in the visual pathway, not in the optics of the eye.

Logo++

2007-10-11T10:41:00.000-04:00

Logo++ is an interpreter for drawing graphical figures following very simple instructions. Though it lacks many essential features of programming languages, it remains a funny start for beginners in computer programming, particularly for kids.

Internet gets first full census for 25 years

2007-10-11T09:20:00.000-04:00

An electronic census of the internet's 2.8 billion addresses has been completed by US researchers. It is the first attempt to contact every web address since 1982 – the results could help tackle the problem of the supply of unique internet addresses running out.

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Peanut Software

2007-10-10T16:04:00.000-04:00

Peanut Software contains a number of free Windows mathematical software, including: Wingeom, Winplot, Winstats, Winarc, Winfeed, Windisc, Winlab, Winmat, and Wincalc.

IFS Construction Kit

2007-10-10T13:08:00.000-04:00

IFS Construction Kit can be used to design and draw fractals based on iterated function systems. The program consists of three main windows. The IFS Window is where you can see and edit the code for the transformations that comprise the IFS. This window also shows the scale used in the other two windows. The Design window shows the effects of the transformations on an initial polygon. You can translate, scale, rotate, stretch, or shear transformations using the mouse, keyboard, or through a dialog box. This provides a way to define or modify transformations without having to enter the numbers in the IFS window. The Fractal window is where you draw the fractal obtained by iterating the transformations in the IFS, either by using the Random Algorithm or the Deterministic Algorithm.

A Prayer for Archimedes

2007-10-10T12:40:00.000-04:00

A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.

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Science and the Islamic world—The Quest for Rapprochement

2007-10-09T16:12:00.000-04:00

Interesting reading on why science and math vanished in the Middle East.

JW's Pictures and Patterns Site

2007-10-09T15:49:00.000-04:00

JW's Pictures and Patterns Site has some interesting mathematically related information, including the 3x+1 problem, with observations and analysis, Pythagorean triples, and much more.

Metamath Proof Explorer

2007-10-09T15:46:00.000-04:00

Inspired by Whitehead and Russell's monumental Principia Mathematica, the Metamath Proof Explorer has over 6,000 completely worked out proofs in logic and set theory, interconnected with over a million hyperlinked cross-references. Each proof is pieced together with razor-sharp precision using a simple substitution rule that practically anyone can follow, not just mathematicians. Every step can be drilled down deeper and deeper into the labyrinth until axioms of set theory—the starting point for all of mathematics—will ultimately be found at the bottom. You could spend literally days exploring the astonishing tangle of logic leading, say, from 2+2=4 back to the axioms.

Wolfram 2,3 Turing Machine Research Prize

2007-10-05T08:50:00.000-04:00

A universal Turing machine is powerful enough to emulate any standard computer.
The question is: how simple can the rules for a universal Turing machine be?

Since the 1960s it has been known that there is a universal 7,4 machine. In A New Kind of Science, Stephen Wolfram found a universal 2,5 machine, and suggested that the particular 2,3 machine that is the subject of this prize might be universal.

The prize is for determining whether or not the 2,3 machine is in fact universal.

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Mike's Math

2007-09-17T10:55:00.000-04:00

"My name's Mike Byster, and according to psychologists … I have one of the fastest mathematical minds in the world."

This is what Mike Byster told students at his "Mike's Math" seminars, and he wasn't exaggerating.

Mike Byster is a math teacher, but he's also a human calculator. He can answer complex math problems in front of his students instantaneously: Miss Lewis: "999 divides by 56?" Byster: "That equals 17.83928571."

Click here for more information.

Click here for Mike's website.

International Mathematical Olympiad 2007, Hanoi-Vietnam

2007-09-04T23:30:00.000-04:00

The International Mathematical Olympiad is an annual mathematical Olympiad for high school students, and every year it is hosted by a different country. Some countries have been the host nation for more than 1 time as Romania, USSR, Hungary, Czechoslovakia, Poland, Germany, Bulgaria, Yugoslavia, United Kingdom, USA. The year 2007 marks the first time that Vietnam was the host country for the IMO - the 48th International Mathematical Olympiad, Hanoi, Vietnam, 19-31 July, 2007.

Periodic Table of Mathematicians

2007-09-04T22:37:00.000-04:00

The Periodic Table of Mathematicians is a collection of facts on various mathematicians put in a periodic table format.