Experimenting with functions to draw thick lines. If you supply limits via "if |x| < 2", etc., you can cut off the lines where you want. So with a little more...
Work-in-progress towards illustrating the relationship of vectors, parallelograms, and determinants. This all started because I was trying to see why the...
Some more examples of the hyperbolic paraboloid (saddle shape). I'm still trying to figure out the easiest way to have the cylindrical gridlines and coloring...
Some more examples of the hyperbolic paraboloid (saddle shape). I'm still trying to figure out the easiest way to have the cylindrical gridlines and coloring...
A first step to graphing symmetrical polyhedra using permutation and reflection matrices. Obviously, I'm not getting the same polyhedron by rotating the first...
Finally got a way to have a fixed-distance inset for parallelogram interiors, so borders don't get obscured. Shouldn't be hard to apply to triangles, and...
... I meant to say: "The minus sign occurs because of the way the angle q is actually the angle of the B vector minus the angle of the A vector. Hope to work ...
Hello, A teacher recently sent me this <http://www.pacifict.com/Examples/Skateboarder/index.html> created by one of her seventh grade students. I've started a...
Use the "n" slider and the "a" slider to see how the "hyperbolic shear" (the Lorentz transformation) keeps the area of the inscribed parallelogram the same,...
Here, we're comparing the areas when the two points are on the same branch of the same hyperbola. Note that in this case, the area of the Lorentz-transformed...
Relevant to my previous postings, here are the angle-sum formulas for hyperbolic functions. These lead to different dot-product and determinant forms for...
Hi, attached is a file showing a nice parametrization of the pseudo sphere, and its relation to the upper-half-plane model of hyperbolic space. Naturally, the...
Don't know if I passed this along, but here's an interesting file to play with. You can twist the red ellipse via the animation slider. If I set the height of...
Ron, ... Very interesting talk. I'm especially glad to here you say that one of your top goals for GC is to have students be able to refer to some problem in...
Hi, We had to swap the oldest childs ibook for a pc laptop - after a YEAR the tech guys still hadn't managed to make the signal strong enough to get to boys...
Chaim, Please excuse the rambling nature of this e-mail; I'll try to tidy things up later. I'm just trying to get out what seem to me to be some interesting...
If you put colored contour lines inside a translucent, high-resolution version of the surface, you get a more 3D effect, I think. There are two plots of the...
You can reset the Animation Slider (via Math/Slider Values) to temporarily override any sliders or other settings you've got for a variable. Below, I've set...
Using different hues around the band helps keep straight what side you're looking at. In the case of an extra half-twist, there's only one side, and hence the...
Don't think this necessarily has any deep significance, but it looks cool. All I did was exchange the coordinates in the function definition. A function in...
I got a question about methods for graphing rays around the origin, and have been experimenting with different ways of plotting spirals and accompanying...
Hello, Flavors of Geometry is a great book, isn't it? Attached are some files illustrating a construction from John Stillwell's The Geometry of Surfaces. The...
Taking Chaim's very helpful files and just re-working them a little, I noticed that the thing about evolutes is that they give you a way to construct curves of...
I'm trying to plot curves on the modular surface for sine(x+iy) that look like the diagram in the Jahnke and Emde book "Tables of Functions", page 67. If...
There was recently on the Group Post a mention of that wonderful curve, the catenary. One its most popular properties is that a car with square wheels will...
