Thursday, December 13, 2007

'Mathlete' Smashes Human Calculation Record

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.

Tuesday, December 11, 2007

Voyager 2 Probe Reaches Solar System Boundary

Heliosphere
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.

Monday, December 10, 2007

VisIt

VisIt
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.

Friday, December 07, 2007

Polyhedra.org

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

Thursday, December 06, 2007

The Universal Digital Library

The Universal Digital Library
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.

Sunday, December 02, 2007

Saturday, December 01, 2007

The Descartes Circle Theorem

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

Crayon Physics Deluxe

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.

Tuesday, November 27, 2007

Möbius Transformations Revealed

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.

Thursday, November 15, 2007

Surfer dude stuns physicists with theory of everything

The E8 pattern (left), Garrett Lisi surfing (middle) and out of the water (right)
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.

Sunday, October 28, 2007

Dataplot

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

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

Wednesday, October 24, 2007

The Simplest Universal Turing Machine Is Proved

2,3 Turing Machine
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).

Friday, October 19, 2007

Islamic Star Patterns

Islamic Star Patterns
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.

Thursday, October 18, 2007

World Digital Library

World Digital Library
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.

Friday, October 12, 2007

Brain Man

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.

Click here for more information.

Optical Illusions and Visual Phenomena

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.

Thursday, October 11, 2007

Logo++

Logo++
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

This colour coded map encompasses the 2.8 billion unique internet addresses and could help chart the spread of computer viruses.
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.

Click here for more information.

Wednesday, October 10, 2007

Peanut Software

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

IFS Construction Kit

IFS Construction Kit
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

700-Year-Old Book
Hidden Text

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

Click here for more information.

Tuesday, October 09, 2007

Science and the Islamic world—The Quest for Rapprochement

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

JW's Pictures and Patterns Site

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

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.

Friday, October 05, 2007

Wolfram 2,3 Turing Machine Research Prize

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.

Click here for more information.

Monday, September 17, 2007

Mike's Math

"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.

Tuesday, September 04, 2007

International Mathematical Olympiad 2007, Hanoi-Vietnam

48th International Mathematical Olympiad
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

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

Tuesday, August 28, 2007

Math Genius Wins University Place, Aged 9

A nine-year-old math prodigy was Thursday admitted to a Hong Kong university, telling reporters he struggled to communicate academically with his own age group.

March Boedihardjo, an Indonesian-Chinese boy resident in Hong Kong, earlier this month gained two grade As and a B in his A-levels -- normally taken by 18-year-olds -- enough for a place at Hong Kong Baptist University (HKBU).

Click here for more information.

Tuesday, August 21, 2007

Arabic Geometry

Catnaps.org has an interesting article on Arabic geometrical patterns.

Thursday, August 16, 2007

Mind and Visual Puzzles

Archimedes' Laboratory
Archimedes' Laboratory provides puzzles, brain teasers, and mental activities to keep your brain young and active.

Thursday, August 09, 2007

EquationSheet.com

EquationSheet.com
EquationSheet.com allows you to create a customized equation sheet from various mathematics and physical equations and constants.

Thursday, August 02, 2007

The Coq Proof Assistant

Coq
Coq is a formal proof management system: a proof done with Coq is mechanically checked by the machine. In particular, Coq allows:
  • to define functions or predicates,
  • to state mathematical theorems and software specifications,
  • to develop interactively formal proofs of these theorems,
  • to check these proofs by a relatively small certification "kernel".

Saturday, July 21, 2007

The Human Geometry

The Human Geometry Project celebrates mathematical art, music, dance and literature through exploration of the human form. And for more risqué pictures, visit Naked Geometry.

Thursday, July 19, 2007

Mapping A Medusa: The Internet Spreads Its Tentacles

The Internet
CHARTING A COURSE. A new map of the Internet shows a core containing the most tightly connected subnetworks (red), while the least-connected subnetworks lie at the edge (purple).
After enlisting the help of thousands of volunteers to track how digital information weaves around the world, researchers can offer a new simile: The Internet is like a medusa jellyfish. It has a dense core surrounded by a highly connected body, from which tentacles dangle.

Click here for more information.

Friday, July 13, 2007

Gato (Graph Animation Toolbox)

Gato
Gato - the Graph Animation Toolbox - is a software which visualizes algorithms on graphs. Graphs are mathematical objects consisting of vertices and edges connecting pairs of vertices: think of cities as vertices and interstates as edges connecting two cities. Algorithms might find a shortest path - the fastest route - or a minimal spanning tree or solve one of other interesting problems on graphs: maximal-flow, weighted and non-weighted matching and min-cost flow. Visualisation means linking cause - the statements of an algorithm - immediately to an effect - changes to the graph the algorithm has as its input - by terms of blinking, changing colors and other visual effects.

Galaxy Zoo

Welcome to GalaxyZoo, the project which harnesses the power of the internet - and your brain - to classify a million galaxies. By taking part, you'll not only be contributing to scientific research, but you'll view parts of the Universe that literally no-one has ever seen before and get a sense of the glorious diversity of galaxies that pepper the sky.

Wednesday, July 11, 2007

Minimal Primes

Jeffrey Shallit wrote a very interesting paper on minimal primes. The PostScript file can be downloaded here.

To print, you can use the free Windows printing utility PrintFile.

Tuesday, July 10, 2007

ZipCode Census Dashboard

The ZipCode Census Dashboard is a flash application that displays U.S. census statistics.

Monday, July 09, 2007

NASA MathTrax

NASA
MathTrax is a graphing tool for middle school and high school students to graph equations, physics simulations or plot data files. The graphs have descriptions and sound so you can hear and read about the graph. Blind and low vision users can access visual math data and graph or experiment with equations and datasets.

Tuesday, July 03, 2007

Mathematical Visualization Toolkit

Mathematical Visualization Toolkit
The Department of Applied Mathematics in the University of Colorado at Boulder provides an interesting Mathematical Visualization Toolkit for visual learning of Calculus and Differential Equations by students.

Friday, June 29, 2007

Thursday, June 28, 2007

Everything Mathematical

MathematiciansPictures.com is a website about everything mathematical (pictures, t-shirts, etc.). If you're into math, you wouldn't be here otherwise, then visit that site for some neat stuff. Just come back afterwards. :-)

E-Tutor Graphing Calculator

E-Tutor has a nice, online, graphing calculator for visualizing equations.

Wednesday, June 27, 2007

Graph Layout Engine (GLEE)

GLEE
GLEE is a .NET tool for graph layout and viewing. It has been developed in Microsoft Research by Lev Nachmanson. GLEE is built on principles of the Sugiyama scheme; it produces so called layered, or hierarchical, layouts. This kind of a layout naturally applies to graphs with some flow of information. The graph could represent a control flow graph of a program, a state machine, a C++ class hierarchy, etc.

Texmaker

Texmaker
Texmaker is a free LaTeX editor, that integrates many tools needed to develop documents with LaTeX, in just one application.

Tuesday, June 26, 2007

WZGrapher Function Grapher

WZGrapher
WZGrapher is an easy-to-use and small-footprinted Function Graphing and Calculation Program written in C language, with capabilities to plot both cartesian and polar functions. WZGrapher can also be used to graph numerical solution curves of integrals, to solve numerically and graph ordinary differential equations up to the fifth order, and to calculate value tables (also of ODEs) including the first derivative values.

Monday, June 25, 2007

Orrery

Ferguson's Orrery
An orrery or planetarium is a mechanical contrivance that reproduces the motions of the planets and, sometimes, of their satellites. Operated by hand using cranks or clockwork mechanisms. More information can be found here and here.

Sunday, June 24, 2007

Vedic Mathematics

Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras, or word-formulae. For example, "Vertically and Crosswise" is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution.

Here are some tutorials on it and some more information.

Group Explorer

Group Explorer
Group Explorer is mathematical visualization software for the abstract algebra classroom. It helps the user visualize group theory, builds students' intuition, and enables experimentation with groups.

Mathematical Illustrations

Mathematical Illustrations
Mathematical Illustrations is a book on mathematical PostScript programming and geometry. The website contains plenty of examples for downloading.

Binary Marble Adding Machine

Binary Marble Adding Machine
This is a very cool description of an adding machine. Check out the original as well.

SITMO

SITMO is a LaTex equation editor. Check out the rest of their website for some other mathematical topics.

Public Implementation of a Graph Algorithm Library and Editor

P.I.G.A.L.E.
P.I.G.A.L.E. is a graph editor and a C++ algorithm library essentially concerned with planar graphs. The editor is particularly intended for graph theoretical research.

Thursday, June 14, 2007

Puzzlers Paradise

TreePuzzlers Paradise
Puzzlers Paradise is a website with some great, interactive, logic puzzles.

Monday, June 11, 2007

PlotKit - JavaScript Chart Plotting

PlotKit is a Chart and Graph Plotting Library for JavaScript. It has support for HTML Canvas and also SVG via Adobe SVG Viewer and native browser support. Requires MochiKit - A lightweight JavaScript library.

Friday, June 08, 2007

WIRIS CAS Web Calculator


WIRIS CAS is an on-line platform for mathematical calculations designed for education. It is in fact a CAS that also includes a DGS inside. You can access a powerful calculation toolbar through an HTML page that includes integrals and limits calculation, function graphing in 2D or 3D or symbolic matrices manipulation. It covers all mathematical topics from High School to University level (Calculus, Algebra, …).

Thursday, May 31, 2007

Scientist Solves Rubik's Cube In 26 Moves

It’s a toy that most kids have played with at one time or another, but the findings of Northeastern University Computer Science professor Gene Cooperman and graduate student Dan Kunkle are not child’s play. The two have proven that 26 moves suffice to solve any configuration of a Rubik's cube – a new record. Historically the best that had been proved was 27 moves.

Rubik's Cube, invented in the late 1970s by Erno Rubik of Hungary, is perhaps the most famous combinatorial puzzle of its time. Its packaging boasts billions of combinations, which is actually an understatement. In fact, there are more than 43 quintillion ($4.3252 \times 10^19$) different states that can be reached from any given configuration.

Full article here.

Wednesday, May 30, 2007

TTCalc

TTCalc
TTCalc is a new mathematical calculator. It has a nice user interface, formulas for calculating can be inserted by using a keyboard or a mouse. The result is automatically shown in a second window without using any additional keys such as 'equal'. The program possess trigonometric functions, inverse trigonometric functions, hyperbolic functions, logical operators, logarithms, functions for converting between degrees and radians and so on. Additionally the program allows the user to define his own variables and functions. Calculations are performed by using floating point numbers with three kind of precision, the biggest has 288 bits for its mantissa and 96 bits for its exponent that is about 2.551…e+11925026709067095507636213441 with 85 valid decimal digits. The program independently allows to insert and display values with the base (radix) from two to sixteen.

Scythe Statistical Library

The Scythe Statistical Library is an open source C++ library for statistical computation, written by Daniel Pemstein (University of Illinois), Kevin M. Quinn (Harvard University), and Andrew D. Martin (Washington University). It includes a suite of matrix manipulation functions, a suite of pseudo-random number generators, and a suite of numerical optimization routines. Programs written using Scythe are generally much faster than those written in commonly used interpreted languages, such as R and MATLAB, and can be compiled on any system with the GNU GCC compiler (and perhaps with other C++ compilers). One of the primary design goals of the Scythe developers has been ease of use for non-expert C++ programmers. We provide ease of use through three primary mechanisms: (1) operator and function over-loading, (2) numerous pre-fabricated utility functions, and (3) clear documentation and example programs. Additionally, Scythe is quite flexible and entirely extensible because the source code is available to all users under the GNU General Public License.

Saturday, May 26, 2007

SAGE

SAGE
Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.

Thursday, May 24, 2007

Graph Sketcher

Graph Sketcher lets you make elegant and precise graphs in seconds, simply by sketching what you want.

Wednesday, May 16, 2007

The Alphabet

The Alphabet Family Tree
What is mathematics without language? What is language without the alphabet? Although, they are somewhat independent of each other since one can count without words and speak without writing, they are not mutually exclusive. The image above was taken from the Phoenician Encyclopedia website, the world's largest web compilation of Phoenician resources & studies.

Tuesday, May 15, 2007

Fractal Land

Fractal Land
Fractal Land is were you will find fractal images done with UltraFractal, Fractint, Apophysis & other fractal softwares, and also some links to fractal resources, tutorials and other fractal galleries.

There are two main galleries: The Images and Fractint Images.

I Heart Mathematics

I Heart Mathematics
Saw this on the web recently and thought it was cool.
Instead of using $\pm\frac{4}{5}$ for the y-intercept though, the golden ratio φ = $\frac{1\pm\sqrt{5}}{2}$ should have been used for a more natural beauty. Also, what would the equation be in 3D?

Friday, May 11, 2007

MPFRCPP

The Multiple Precision Floating-Point Reliable Library C++ Interface (MPFRCPP) is free object oriented interface to the MPFR library. MPFR provides arbitrary precision arithmetic on floating-point numbers. MPFRCPP overloads operators, functions and represents floating point numbers as class objects to make using of MPFR in OO-programs easier.

Distribution package includes Numeric Analysis / Computer Research C++ Classes with implementation of rational numbers, polynomials (including orthogonal polynomials) and complex numbers.

Wednesday, May 09, 2007

The Simpsons

Fermat's Last Theorem
Euler's Formula
The longest running animation TV show of all time and one of the best cartoons ever. Known for covering humor on every subject. Here' are a couple on Fermat's Last Theorem, Euler's Formula and the Complexity classes P and NP.

Interplanetary Transport Network

Interplanetary Transport Network
The Interplanetary Transport Network (ITN) is a collection of gravitationally determined pathways through the solar system that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space can be redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them even though there is no material object at them.

Factorization Using the Elliptic Curve Method

Click here for a Java implementation of integer factorization using the elliptic curve method (ECM). Source code included.

Prime Number Spiral

Prime Number Spiral
The Prime Number Spiral software is a tool for exploring the Ulam spiral.

Monday, May 07, 2007

Gnuplot

Gnuplot is a portable command-line driven interactive data and function plotting utility for UNIX, IBM OS/2, MS Windows, DOS, Macintosh, VMS, Atari and many other platforms. The software is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally intended as to allow scientists and students to visualize mathematical functions and data. It does this job pretty well, but has grown to support many non-interactive uses, including web scripting and integration as a plotting engine for third-party applications like Octave. Gnuplot has been supported and under development since 1986.

Saturday, May 05, 2007

Project Euler

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

Friday, May 04, 2007

uCalc

UCALC Windows Graphing Calculator
UCALC Windows Graphing Calculator comes with the following features: Expression Evaluator, Unit Converter, User Solution Modules, Graphing, Equation Solver, User Functions & Variables, Summation Tables, Integrator, and General Ledger.

UCalc Fast Math Parser
UCalc Fast Math Parser allows programs to evaluate math expressions that are defined at run time. Ease of implementation, flexibility, sturdiness and speed are at the core of the product's design. It includes direct support for Visual Basic, C++ (Microsoft and Borland), PowerBASIC (PB/DLL and PB/CC), and Delphi.

Euler Angles

Euler Angles
A good read on three-dimensional space and how to rotate the orthogonal coordinate system.

Command Line Quaternions

Quaternions are numbers with 4 parts: one for time, three for space. This project hopes to create command line functions that generate thousands of points of quaternions, to be fed into animation software. Think: analytical animation!

Wolfram Web Resources

In addition to Mathworld, Wolfram Web Resources hosts an extensive list of other sites, including: Demonstrations, Functions, Gallery, Integrals, and Tones,

Thursday, May 03, 2007

Mathematica 6

Mathematica 6 has been released and you can see some nice demonstration over at the Wolfram Demonstration Project.

Calculus Videos

The Department of Mathematics at University of Houston has created this library of calculus videos viewable using Apple's QuickTime. They also have a list of shorter videos for some calculus concepts.

Wednesday, May 02, 2007

Gnofract 4D

Gnofract 4D is a free, open source program which allows anyone to create beautiful images called fractals. The images are automatically created by the computer based on mathematical principles. These include the Mandelbrot and Julia sets and many more. You don't need to do any math: you can explore a universe of images just using a mouse. It runs on Unix-based systems such as Linux and FreeBSD.

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.