Work in progress towards graphing the "canonical forms" of the quadric surfaces, but in parameterized cylindrical coordinates, not rectangular ones, so the...
Not sure exactly what the 28 real-valued tangents in question fit in here, but here's an example of the intricate effects you can get with inequalities and...
Just saw the "shaders" in action a late-model Mac. Talk about breath-taking! The field lines one is the most vivid image I've seen of this kind of thing. ... ...
Work in progress on comparing rotations to area-preserving shears, and along the way, hyperbolic arc-length to circular arc-lengths, hyperbolic inner-product...
Sorry if I muddied the waters re linear transformations. http://mathworld.wolfram.com/LinearTransformation.html ... But how about reducing this to plain(er)...
Haven't quite got it working yet, but here's an example where the same transformation is applied, but with the square rotated 45 degrees beforedhand, to show...
Does it specify it completely to say that the Lorentz transformation maps a grid of rhombuses to another grid of rhombuses, each rhombus in the second grid...
A preliminary version of what is essentially the same transformation as the "Lorentz transformations" I posted earlier. The differences are the orientation of...
Trying to find a way to get the coloring to come out right. In the course of doing this graph, I was reminded that the angle that acts as the parameter here...
This is the analog to the case of the ellipse parameterized by the angle in its scribed circles (= "right-angled ellipse"). If we put the other branches in,...
Morph from ellipse to hyperbolas, with the equiangular major and minor ellipses morphing to the corresponding hyperbolas. Does the above morph qualify as a...
Here's an attempt to trace arc-length on the ellipses and hyperbolas. I've thickened the principal ellipse and hyperbolas. Problem: It's not working when comes...
... The only limitation is, you can't use transparency in the same file, it seems. The image below, without transparency, gets cut off sharply:  But the...
Work in progress towards a way to plot surfaces more clearly. For the hyperbolic paraboloid (shape like a Pringles chip in yellow), it's shown how it can be...
Work in progress towards clearer ways to show projected lines, etc., so you can see exactly which line is which even when they overlap. Ellipse is thickened...
More examples of how much sharper is with the newer Macs. Not a big problem, but it looks like the checkered surface is getting "overlap" from the colored...
The drawing of the color maps with the varied saturation is really slow, but it does look nice. I'm trying to come up with techniques that will show just what...
I'm unable to view graphics that are posted in many of the messages. I keep getting a message like Attachment(not stored) pastedGraphic2.tiff Type: image/tiff ...
You just have to set the way you receive e-mails from the Yahoo group to individual e-mails. If the graphics are in e-mails I sent, I can forward them to you....
I have been playing with Hypotrochoids and Epitrochoids, and wanted to share the results with everyone. Hypocycloids are the curves traced by a single point on...
Matthew, I believe that this group has attachment saving turned off. You have to have the messages mailed to you (I think it has to be individual mail, not ...
I use GC to draw graphs to use on assignments, quizzes, and tests. Some times I would like the graphs to be thicker for more of a contrast when photocopying....
Rodney, Here is a trick that MAY or MAY NOT be useful... I use Shift-PrtScn on the keyboard to capture the image, use Microsoft Paint to paste and crop the...
Just to clarify, this file shows the simultaneous graphs of the epitrochoid---the gray circle rolling outside the blue circle---and the hypotrochoid---the gray...
I'm trying to find an efficient way to get the angle of points that get dragged around. For some reason, GC returns a non-zero imaginary value for what seem to...
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