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The power of ideas to transform the world is itself accelerating. -Ray Kurzeweil, The Singularity is Near
0, 1, 1, 2, 3, 5, 8, 13, 21, 34,...
xn = xn-1 + xn-2

Math tools

Tuesday, 19 September 2006 21:42
Project Euler - just cause.

Math Packages

Octave
Madagascar - package for multidimensional data analysis and reproducible computational experiments.
ASCEND - ASCEND can solve systems of non-linear equations, linear and nonlinear optimisation problems, and dynamic systems expressed in the form of differential/algebraic equations.


Visualization

Lately I've been trying to communicate complicated geometric problems with co-workers who are remote workers. If we worked together in a normal office enviroment, we would simply use a white board...
GeoGebra - an open source
CABRI3D - Cabri 3D is a 3-dimensional commercial interactive geometry software
The Geometer's Sketchpad
Dynamic Geometry - Home - Silverlight 2 and C# 3.0 computer model of plane geometry that allows you to create interactive ruler and compass constructions and experiment with them.
Antiprism - Polyhedron Modelling Software - Create, transform, analyse, and visualize polyhedra.

Hilbert II - a program suite that enables a mathematician to put theorems and proofs into that knowledge base.
Tac - A generic and adaptable interactive theorem prover

Sage: Open Source Mathematics Software
graph.tk - graph.tk/about, which aantthony/graph.tk apparently is being superseded by aantthony/javascript-cas.

JSXGraph | Dynamic Mathematics with JavaScript - interactive geometry, function plotting, charting, and data visualization in a web browser.
sketchometry - built using JSXGraph
Main Page - JSXGraph Wiki


Latex || LaTeX || TeX (rhymes with blechhhhh)

mathematical typesetting
you might have noticed, I'm a MathJax fan, since it is randomly displayed on my site. here is some info on MathJax, and some example usage...
1 . $a^2 + b^2 = c^2$ 2 . $ax^2 + bx + c = 0$ 3 . $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ 4 . $m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{\Delta y}{\Delta x}$ 5 . $f'(x) = \lim\limits_{\Delta x \to 0} \dfrac{f(x+\Delta x)-f(x)}{\Delta x}$ 6 . $\dfrac{d}{dx} \left [[x^n \right ] = nx^{n - 1}$ 7 . $\int_a^b f(x)~dx = \left [[F(x) \right ]_a^b = F(b) - F(a)$ 8 . $\int_a^b f(x)~dx = f(c)(b - a)$ 9 . $\text{average value} = \dfrac{1}{(b-a)} \int_a^b f(x)~dx$ 10 . $\dfrac{d}{dx} \left [[\int_a^x f(t)~dt \right ] = f(x)$
MathJax - MathJax is an open source JavaScript display engine for mathematics that works in all browsers.
Wiki MathJax Syntax - the above samples come from this page, you'll want to note the use of ?config=TeX-AMS-MML_HTMLorMML on the MathJax.js request. this loads TeX/AMSmath.js defining /dfrac, resolving your "undefined control sequence \dfrac" error. It also brings in AMSsymbols.js and some other javascript relating to error handling.
Martin's MathJax Guide - Introduction
TeX Commands available in MathJax - very large example page
MathB.in - Math pastebin with LaTeX and Markdown support - TeX Samples - MathB.in Getting started - MathB.in(uses MathJax internally)

LaTeX/Mathematics - Wikibooks, open books for an open world
MathLex - Demo
Detexify LaTeX handwritten symbol recognition - draw the symbol you are looking for into the square area above and look what happens!


Wolfram Alpha

Last Lights On - Mandelbrot fractal zoom to 6.066 e228 (2^760) on Vimeo
Wolfram Alpha Opens API, More Features on the Way

R Programming (Statistics)

The R Project for Statistical Computing
Download R Now | inside-R: A Community Site for R
Revolutions - News about R, statistics and the world of open source from the staff of Revolution Analytics


Programming Libraries

Main Page - Eigen - Eigen is a C++ template library for linear algebra: vectors, matrices, and related algorithms.
Math.NET Project
Ceres Solver - non-linear least squares solver - QR,Cholesky, specialized Schur
ceres-solver - A Nonlinear Least Squares Minimizer - Google Project Hosting - C++ deps: cmake,Eigen3,google-glog,gflags,SuiteSparse,CXSparse,BLAS,LAPACK
Perl Data Language - compactly store and speedily manipulate the large N-dimensional data arrays - Perl Data Language (PDL) Scientific computing with Perl
The PDL Book (PDF)


Fourier

Twisted Documentation: Waves and Harmonics - The book "Who is Fourier, a Mathematical Adventure" is a cool book...
An Interactive Guide To The Fourier Transform | BetterExplained


Math viz

Toys - Jason Davies - Mathematical Visualisations The majority are written in JavaScript and require a modern browser with support for SVG or canvas. Enjoy! (neat!)
MuZuu - Spiralsymmetry (in a very small and discrete world)



quasicrystals

We Alone on Earth: quasicrystal - Visual Analogue of a Shepard Tone
main is usually a function: Quasicrystals as sums of waves in the plane
kmcallister/propane · GitHub - Propane is a system for functional synthesis of images and animations. (Haskell) In spirit of Pan, Propane uses the Repa array library. This means that Propane automatically uses multiple CPU cores for rendering, provided the program is compiled and run with threads enabled. That said, the implementation has not yet been optimized for speed.
The Pan Home Page - Pan is an experimental embedded language and compiler for image synthesis and manipulation, based on principles from functional programming. (Haskell)


fractals

We Alone on Earth: Jython and Feedback Fractals in 42 Lines
The beauty of the Mandelbrot set - Last Lights On - Mandelbrot fractal zoom to 6.066 e228 (2^760) on Vimeo
Mandelbrot Set Renderer using JavaScript and the Canvas API - Geoff's Mandelbrot Renderer.
bugman123.com - Paul Nylander’s Web Site
An Introduction to the fascinating patterns of Visual Math
Dimensions Home - Mathematical vertigo guaranteed!
Mathematical imagery by Jos Leys.
Mac App Store - Scale: Beautiful Fractals Michael Fogleman
Newton fractal - Wikipedia The fancy header image | Almost looks like work
Git fractals - Sierpi?ski triangles using Git. Cayley graph of F2


Sequences and Series

The On-Line Encyclopedia of Integer Sequences® (OEIS®)


Lindenmayer System || L-System

L-system - Wikipedia, the free encyclopedia


Other sites with lists of math tools

Free and Open Source Math Programs - IMHO
Open-source mathematics | wdjoyner.org

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Last Updated on Tuesday, 16 September 2014 23:33