Start Calculator


A Geometric Calculator

The geometric calculator is just an ordinary desk calculator that uses the Clifford Numbers over a three dimensional Euclidean Space.

This means that in addition to doing the normal computations on (computer implemented) real numbers that you are used to finding on a desk calculator, this calculator also computes on vectors in two and three space, on the bivectors over those vectors, on the trivector over three space, on complex numbers, and on quaternions.

Now, that may be so much gobbledy gook to you, it was to me once, but this set of computations is pretty interesting in that it includes a lot of the practical computations that people have learned to do in the past few millenia: computing areas and volumes, surveying, planar navigation, celestial navigation, satellite control, robotics, computer graphics, and more.

One way to put it is that numbers can be more than simply magnitudes, we can have numbers with intrinsic shapes, such as pointy numbers, flat numbers, solid numbers, and round numbers. The pointy numbers are more commonly called vectors, at least by that part of the population which calls them anything at all. They are pointy because they simply point in some direction. If we take two pointy numbers which point in different directions, we can combine them to make a flat number, also known as a bivector. This operation, combining two pointy numbers to get a flat one, is called the wedge or outer product, and it's key on the calculator is labelled with something like ^. The magnitude of a flat number is an area, the area of a parallelogram defined by the two pointy numbers wedged together. If we're working in three dimensions we can wedge a third pointy number onto the flat number to get a solid number, also known as a trivector. The magnitude of the solid number is the volume of the parallelopiped defined by the three pointy numbers wedged together.

I don't have a cute vulgarization to explain the round numbers, yet. So you will have to take my word that if you combine a simple magnitude with a flat number you get a number which can be used as an operator which scales and rotates pointy numbers and flat numbers. Round numbers are also known as complex numbers and as quaternions.

My apologies for the incompleteness of all this. There's a lot more to be said, but other duties call. And I have a terrible time figuring out who I'm writing this for, the first question any author really ought to answer.

To allow you to experiment with the calculator as a local application, I have made a jar file with all you need to run the calculator. The jar unzips (using the usual cast of unzip utilities) to create a directory named "calculator" which contains, among many other files, a file named "index.html" which has a link to start the calculator window.

Roger E Critchlow Jr
Last modified: Mon Aug 25 20:17:00 MDT 2003