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.