Calculon 
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Calculon is three things: A tool, an educational resource, and a superbly engineered demo of the power of the Zaurus.
 
The Tool
Calculon is a program for plotting mathematical functions which describe points, lines or surfaces in 2, 3, 4 or any number of dimensions. Equations are entered in natural and correct mathematical format via a powerful editor that supports insertion, selection, cut, paste and copy, but with special behaviour tailored for mathematical manipulation. Functions to be plotted can be described by any number of cross-referring equations, parametric plots are seamlessly supported. Any number and mixture of functions can be plotted simultaneously on the same axes.
 
The Educational Resource
Calculon uniquely arranges its input into free-form worksheets, just like jotting equations on a piece of paper. In addition to equations, text notes and sketches can also be added (see this example worksheet). Calculon worksheets can therefore both present and explain the mathematics behind a function plot, but the important thing is that the plot is actually calculated live from the worksheet. What better way to learn than to fiddle about with the equations and see what happens? (Calculon even provides a special mechanism of "User Controls" to interactively manipulate values). Worksheets can be collected together into Calculon Packages which can be easily transferred to other Calculon users. As the Calculon user-base increases, a substantial base of freely downloadable Packages will be become available (we're already working on some here). Calculon is more than just a mathematical tool, it is a powerful medium for communication. See these Example Worksheets and Plots to get the idea
 
The Demo
Calculon has been highly engineered and optimized to be fast and responsive. The seashell demos supplied with Calculon really show off the power of the Zaurus. The calculation is quick, and the rotations are super-smooth. If you want to show off your PDA to colleages, Calculon will not fail to impress.
 
Quick FAQ
 
Q: I heard PDAs are slow at mathematical calculations?
Pretty much all current top-end PDAs are based on ARM processors which don't have hardware support for floating point numbers. Therefore calculations on real numbers must be done in software, which is slow. Calculon does not use the standard software to do this. Our routines are in some cases up to 50 times faster than the standard ones, with no significant loss of accuracy.
 
Q: I want to see more screenshots and examples.
Have a look here.
 
Q: In what ways can I export work out of Calculon?
Worksheets can be exported as LaTeX or XML (with the equations coded as either Presentation MathML or Content MathML). Worksheets can also be exported as a single large image (see this Example). The actual plots can be exported as images.
 
Q: Sounds great, but how am I going to learn to use it?
Extensive help is provided in the form of two packages which are installed with Calculon. The instructions go through from first principles, and there is a fairly exhastive set of demos which show just about every variation of Calculon's use. Never fear - Calculon is easy to use.
 
Q: I need some support!
First, try here: Calculon FAQ.
If that doesn't help, send an email to: john@vaagmaer.com