Circular studies

I'm currently studying the curvatures of circles in my spare time. I'm doing this by writing geometric modelling software. There is a reason why I'm doing this, but I'll talk about the reasons at some future point.

Below is some output from the tool that I'm currently working on. Click on the images to see them enlarged.

	The three great circles of a sphere.
	I'm looking for a decent representation of scale (of the circumference) of a circle. I accidently stumbled across below whilst messing around. Maybe I can insert direction arrows into each circle. Imagine that this picture is of a globe (please ignore the additional small circle :) and it's got axes through it's poles too. We think of these axes as infinite straight lines, but they are actually infinite circles.
	Sun Feb 24 05:26:15 GMT 2002: A few geometries that I produced during testing.
	Tue Feb 26 11:10:57 GMT 2002: A representation of signals down a line with fixed frequency and various amplitudes, perhaps. You should see this animated; by modulating the size of the circles a represention of amplitude modulation can be made.
	Mon Mar 4 15:40:20 GMT 2002: The orthogonal elements of a sphere are represented in three different colours. The elements are cylindrical and cover the entire surface. The surface is a 3D one. (The picture is slightly confusing because all the rear elements are also visible. The centre of the sphere could do with being less transparent.)
	To make things less confusing we can look at just one element in each orthogonal plane.
	... and then zoom in to see the point on the surface defined. In this case defined in an annular sense.
	... or in a cylindrical sense. The surface point is therefore defined by three orthogonal dimensions. Every point on the surface is defined by a triplet of curvatures. One in each of the red, green and blue directions.

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