Monday, April 30, 2007

SpeQ Mathematics

SpeQ
SpeQ is a small, extensive mathematics program with a simple, intuitive interface. All calculations are entered in a sheet. In there you can freely add, edit and execute all calculations. You can define variables and functions, and plot graphs of your functions. You can save your calculations for later re-use.

Sunday, April 29, 2007

Maths Films

Maths Films
The aim of this website is to provide a source of animated mathematical films, images and text to support the teaching of mathematics in ways that build on the intuitions and powers we have all possessed all our lives.

Saturday, April 28, 2007

What is the 4th Dimension?

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional analogs of three-dimensional objects, e.g. hypercube, hyperplane, hypersphere. n-dimensional polyhedra are called polytopes.

Here are some interesting notes, images and movies for understanding what the fourth dimension would look like.

Mesecina

Mesecina
Mesecina is a software to visualize and study the medial axis and related computational geometry structures in the plane.

Cornell University Library Historical Mathematics Monographs

The Cornell University Library Historical Mathematics Monographs is a collection of selected monographs with expired copyrights chosen from the mathematics field. These were monographs that were brittle and decaying and in need of rescue. These monographs were digitally scanned and facsimile editions on acid free paper were created.

Friday, April 27, 2007

FreeTechBooks.com

FreeTechBooks.com has a large number of free mathematics books.

yEd - Java Graph Editor

yEd
yEd is a very powerful graph editor that is written entirely in the Java programming language. It can be used to quickly and effectively generate drawings and to apply automatic layouts to a range of different diagrams and networks.

Thursday, April 26, 2007

What Do Numbers Sound Like?

This website contains a list of math songs. The numbers assigned are actually the major scale degrees that correlate. If you don't know basic music theory, think "Do = 1, Re = 2, Mi = 3, Fa = 4, So = 5, La = 6, Ti = 7, Do + Octave = 8, Re + Octave = 9, and 0 = Quarter Rest." Listen to $\pi$ up to 1,000 digits on the piano alone or on the piano, bass & flute together.

Open (to interpretation) question: Which number sounds the best? Which transcendental constant sounds the best?

BBP-Type Formulas

The BBP (named after Bailey-Borwein-Plouffe) is a formula for calculating $\pi$ discovered by Simon Plouffe in 1995,
$\pi = \sum_(n=0)^\infty(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6})(1/(16))^n$.

Amazingly, this formula is a digit-extraction algorithm for $\pi$ in base 16.

Following the discovery of this and related formulas, similar formulas in other bases were investigated. This class of formulas are now known as BBP-type formulas.

Functional Programming Library for XSLT (FXSL)

Dimitre Novatchev, the author of FXSL, was kind enough to give a more thorough explanation of what FXSL can do. Here's the current list of all the features.

FXSL has quite a bit of support for Math operations:

  • Exponential and logarithmic functions.

  • Trigonometic and hiperbolic-trigonometric functions.

  • Reverse trigonometric and reverse hyperbolic functions.

  • Finding the root of a function of one real argument using Newton-Raphston and the binary-search algorithms.

  • Generation of sequences of random numbers with values in a given interval and with certain distributions.

  • Numerical differentiation.

  • Numerical integration.

  • Testing primality of natural numbers.

  • Generation of Fibonacci numbers.

An XSL Calculator: The Math Modules of FXSL

Here's a helpful website for doing math problems using XSLT. Section #2 leads to an XSL calculator using the FXSL library.

mimeTex Tutorial

This website offers a LaTex math tutorial for mimeTex. It also has an online editor for you to try out the examples as you learn about LaTex

Mathematics Toolbar

Mathematics Toolbar
The Mathematics Toolbar consists in a Microsoft Word template document (files with extension « .dot ») displaying a special command bar to the user. With the various buttons offered, the user can then create mathematical formula.

Burr Tools

Burr Tools
For people too lazy to solve puzzles themselves, you can use Burr Tools to help solve them for you. This tool is also useful for looking at three-dimensional orthogonal projections.

Infinite Fractal Loop

The Infinite Fractal Loop is a web ring dedicated to fractal art. I found it while browsing Keith's Fractal Art.
Keith's Fractal Art

Wednesday, April 25, 2007

VisualComplexity

VisualComplexity.com is a unified resource space for anyone interested in the visualization of complex networks. They present a large number of network data similar to ManyEyes. An interesting example of visualization can be seen at ZipDecode.

Tuesday, April 24, 2007

Liquid Journey

An interesting website that has some nice mathematical, chaotic animations using flash.

LaTex Equation Editor

This online LaTex equation editor belongs to the Hamline University Physics Department.

Number Systems of the World

Here's a nice collection in different languages of number systems of the world. Granted, this list is not exhaustive and only includes the first hundred integers and zero.

Monday, April 23, 2007

Natural Numbers

Here's an interesting website called NaturalNumbers.org. They have a couple of free programs that deal with primality testing and zeta functions. One of their more interesting pages has an analysis of the first 100 proximate-prime quadratic polynomials for n = 0 to 1000.

Apfloat for C++

Apfloat is a high performance arbitrary precision package. That means you can do calculations involving millions of digits with it. It uses Number Theoretic Transforms. It's simple to use. It's fast. It's freeware.

Number Spiral

Number Spiral
NumberSpiral.com has an interesting report on number spirals which are similar to Ulam's Spiral. The image shown was created using their Vortex application.

More On Ulam's Spiral

Another Java application that can generate Ulam's Spiral.

Saturday, April 21, 2007

LaTex Editor (LEd)

LaTex Editor
LEd, short for LaTex Editor, is a free environment for rapid TeX and LaTex document development.

Primality Testing Using RegEx

Here are a couple of interesting methods for doing primality testing using RegEx in Perl and Python.

Method #1 (Perl):
perl -wle 'print "Prime" if (1 x shift) !~ /^1?$|^(11+?)\1+$/'

Method #2 (Perl):
perl -wle 'print "Prime" if (1 x shift) !~ /^1?$|^(11+?)\1+$/' [number]

Method #3 (Python):
import re
def is_prime(num):
return not re.match(r"^1?$|^(11+?)\1+$", "1" * num)

Tuesday, April 17, 2007

Prime Numbers in PostScript

Here's an interesting website that shows you how to use a printer to generate prime numbers. It also has a PostScript file that generates ULAM's Spiral.

Monday, April 16, 2007

Ulam's Spiral

Ulam's Spiral
Ulam's Spiral, also known as the Prime Spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the spiral. In the right plot above, primes are indicated in red and composites are indicated in yellow.

Le Village Premier has an interesting stand-alone Java application that can generate the spiral.

arXiv.org

The Cornell University Library hosts the arXiv.org website. arXiv.org has open access to hundreds of thousands of e-prints in Physics, Mathematics, Computer Science and Quantitative Biology.

Graph Paper

Here are three sites that allow you to create graph paper: WebEE, Incompetech and PDF Pad.

Use some of the grids to test Ulam's Spiral.

Sunday, April 15, 2007

Leonhard Euler

Leonhard Euler (pronounced Oiler) was born on April 15, 1707 and died on September 7, 1783. He was a Swiss mathematician who was tutored by Johann Bernoulli. He worked at the Petersburg Academy and Berlin Academy of Science. He had a phenomenal memory, and once did a calculation in his head to settle an argument between students whose computations differed in the fiftieth decimal place. Euler lost sight in his right eye in 1735, and in his left eye in 1766. Nevertheless, aided by his phenomenal memory (and having practiced writing on a large slate when his sight was failing him), he continued to publish his results by dictating them. Euler was the most prolific mathematical writer of all times finding time (even with his 13 children) to publish over 800 papers in his lifetime. He won the Paris Academy Prize 12 times. When asked for an explanation why his memoirs flowed so easily in such huge quantities, Euler is reported to have replied that his pencil seemed to surpass him in intelligence. Fran├žois Arago said of him "He calculated just as men breathe, as eagles sustain themselves in the air" (Beckmann 1971, p. 143; Boyer 1968, p. 482).

One of the most famous and appealing equations, $e^{i\pi} + 1 = 0$ (where $e$ is Euler's number, the base of the natural logarithm, $i$ is the imaginary unit, one of the two complex numbers whose square is negative one (the other is $-i$), and $\pi$ is pi, the ratio of the circumference of a circle to its diameter) was derived by him.

Mathematical Association of America (MAA)

The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level. Our members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. We welcome all who are interested in the mathematical sciences.

International Mathematical Olympiad

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 90 countries from 5 continents. The IMO Advisory Board ensures that the competition takes place each year and that each host country observes the regulations and traditions of the IMO.

William Lowell Putnam Mathematics Competition

The William Lowell Putnam Mathematics Competition is a North American math contest for college students. Each year on the first Saturday in December, over 2000 students spend 6 hours (in two sittings) trying to solve 12 problems. Individual and team winners (and their schools, in the latter case) get some money and a few minutes of fame.

The Putnam exam problems and solutions can be found here.

Saturday, April 14, 2007

GeoGebra

GeoGebra
GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus. It received several international awards including the European and German educational software awards.

Create a Graph

The National Center for Education Statistics (NCES), located within the U.S. Department of Education and the Institute of Education Sciences, is the primary federal entity for collecting and analyzing data related to education. A couple of interesting links that they have are a couple of sites to create graphs with flash and without.

Cartoon

Cartoon

Friday, April 13, 2007

Console Calculator

Console Calculator
Console Calculator is a fast and powerful command-line calculator. This calculator performs advanced mathematical functions, remembers recent entries, allows creation of user defined variables and custom functions. This calculator is an especially handy tool for software developers or engineering.

muParser

muParser
muParser is an extensible high performance math parser library. It is based on transforming an expression into a bytecode and precalculating constant parts of it.

MathsNet

MathsNet is an interactive website for learning mathematics. They also have a wide variety of mathematical games and puzzles.

Thursday, April 12, 2007

WisWeb

WisWeb is the website of the Freudenthal Institute for Science and Mathematics for secondary education (students of 12 to 18 years old). The main focus of the site are applets; small computer programs that run over the internet.

Wednesday, April 11, 2007

TiddlyMath

TiddlyMath is a web notebook for mathematics. It allows you to create math formulas, diagrams and graphs to display on the web.

Many Eyes

You can explore data using your eyes! This site is set up to allow the entire internet to upload data, visualize it, and talk about their discoveries with other people.

Goldbach Weave

Goldbach Weave
Check out Andy Wardley's website for an explanation of the Goldbach Weave.

Tuesday, April 10, 2007

Emprise JavaScript Charts

EJSChart is a 100% pure JavaScript charting solution.

Jmath

Jmath is a Computer Algebra System (CAS) targeted at high school students. This one uses Java, but is reasonably fast.

QPlot

QPlot is a nifty little application that allows you to visualize scatter data by entering or digitizing them.

The Perfect Circle

Rumor has it that they hold competitions for who can draw the most perfect circle by hand. No proof of this yet, but watch this video to be impressed.

Math Forum

My Math Forum: for a better understanding of mathematics.

Sunday, April 08, 2007

Magic Number Machine

Magic Number Machine
Magic Number Machine is a free, full-featured, graphically laid out, high-precision, scientific calculator for Mac OS X 10.4 and greater. Full source-code is included with the distribution.

Ideal if you need to enter large expressions or have accurate precision. "Data" drawers allow an easy way to generate statistical data, linear regression and Gaussian elimination. The extensive support of complex numbers and hexadecimal numbers is also a significant benefit for anyone who has to work with this type of data.

Requires Mac OS X 10.4 or greater. Native Intel Mac support (universal binary). Source code requires XCode 2.2 or greater.

Friday, April 06, 2007

TeXclip

TeXclip is the web application for people who prefer TeX than PowerPoint's equation editor.

Thursday, April 05, 2007

Wikisky

Okay, this is not a math post per se, but who doesn't like astronomy? Wikisky can show you the stars above a given location at a certain time. Pan, zoom, browse and explore the night sky using a Google-Earth-like interface.

Wednesday, April 04, 2007

Mathematics in Movies

This site offers some clips of the mathematical scenes from different movies and TV shows. I hghly recommending watching Sneakers (1992), A Beautiful Mind (2001) and Proof (2005).

Monday, April 02, 2007

Goldbach Conjecture: Proved?

The Goldbach Conjecture states that all positive, even integers ≥ 4 can be expressed as the sum of two primes.

Several papers have recently surfaced at arXiv.org claiming to have proved this. However, none of these methods have been verified yet.