... Sorry for the mistake. A tetrahedron-shaped model would, of course, have four rods, each pivoted at the center. This is what happens with tetrahedral...
A group member wrote me that if there are 3 rods (all with like positive charges at their ends) confined to a sphere they would form 3 mutually perpendicular...
Interesting as always, Chris!!!! (and it's OK with the Josˆm although it is Jorge (as you wrote to me).) My idea was in response to the discussion about the...
GraphingCalcUsers: Here is something I came across that might be of interest to anyone teaching geometry who wants to give examples of applications of ...
This one is fun to play around with. Those of you with subscript-enabled versions could extend the iterations out farther without wearing out the alphabet the...
Here's one version of the 3D cube. Finally got all the vertices to "glow" using a separate "corner-bracket" for each vertex. What good is it? The next step is...
[Here's a smaller e-mail with the same contents, essentially. Sorry about the size of the last version.] Here's one version of the 3D cube. Finally got all the...
GC users: I'm having trouble getting the great circles around the cube vertices. It should be possible from the vertex coordinates below. D_t and D_b are the...
Shows a cube cut by a rising plane, which changes color as it rises. (Another great GC feature---the "n" value of the animation slider can be used in...
I thought I might be onto a way to do successive iterations via the animation parameter using the following two-variable "indexed" function, but for more than...
This shows the cross-sections of the cube via filling the circumsphere with water. It's as if the cube is made out of mesh, since the water level rises inside...
I modified the Julia iterations so that you can use another base function, rather than squaring. The example I left for the function made for a neat...
Arne, ... And also good for iterated function analysis and fractals. Ron is working on fixing the bug involving the indexed functions, so it will be possible...
Russ, Very nice, I'm having fun experimenting with it. Maybe it could be put over the plot of the Julia set as a whole, as shown in the nice example from the...
... This is related to Thomson's problem in physics: find the equilibrium configuration of n point charges constrained to a sphere. It's not an easy problem,...
mark snyder
msnyder@...
Dec 13, 2005 5:31 pm
708
Here's a draggable basepoint version of yours, and the original Example. Fun! Russ <<Juliaset,16,draggable.gcf>> <<Draggable Julia Sets>>...
... I look forward to that! I'm learning a lot from you. I admit to some slight guilt that I'm not contributing more, [:-)] but in the end I guess I can't...
A square antiprism of side length 2 Mark, Above is work in progress towards graphing the square antiprism and trying to figure out what relationship this has...
Somebody asked me to recommend a few books on linear algebra and related topics. Here's my list. Any comments or additions would be welcome. For linear algebra...
The hyperbolic color plot in the 3rd quadrant below is produced by: I'm trying to get a one-line function of the u and v parameters that will give me a...
Mark, Thanks for the reply. This is all very intersting stuff, and very relevant to applying geeomtry. A few comments below. ... Thanks, that clears things up...
... If I use the "Thermal Relax" algorithm it looks like I do get the square antiprism. If I use the MC Anneal algorithm, which is I believe supposed to do a ...
Work in progress towards deriving all the coordinates for a cube when we turn it on its diagonal. All coordintates are in terms of the side-length. I'm also...
I'm trying to graph the sector between two arbitrary 3D vectors, in purely vectorial (i.e., coordinate-free) terms. This would be a huge help in visualizing...
I've fixed up the sector drawing here. We get a circular sector with a specified radius, with the hues changing (more or less) every 15û. I want it to go from...
Here's a way to plot a solid sector between any given 3D vectors with a common start point. Very useful for visualizing 3D angles and their transformations. ...
