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

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

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.

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.

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.

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

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.

LaTex Editor (LEd)

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)

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.

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.