By setting the k_2 and k_5 constants you can get the compound-harmonic-motion Lissajous curves in both polar and rectangular coordinates. These may seem like...
... I managed to plot the points and lines, but I'm at a loss as to how to do best-fit plotting for polar coordinates (or in general, for that matter). Any...
I'm just playing around with fitting curves through the points P_1, P_2, and P_3, which are in polar coordinates. I think what I have here is the unique...
... I'll get back to you on that. The easiest way is probably to put the rotation(s) in a function R(theta). Then you can apply is to each point: R(theta) A,...
I would like to note that GC has the option to select an equation and Copy as Text to make a text (ascii) copy of the equation. This can be pasted in some...
It looks like the Archimedean spirals of different powers are the analogs of the different powers of a linear variable. Therefore, it seems like a safe bet...
Forgot to mention: the above included the assumption that the Lagrange interpolation polynomial converges to the Taylor series as the interpolation points come...
I may have to eat my words from the last e-mail. Maybe the spiral interpolator doesn't automatically produce conic sections the way I thought. It looks like it...
You can get a closer approximation of the target curve (a hyperbola, in this case) by enlarging the graph and also by using the symmetry of the dotted curves...
I also said some misleading things about complex-number Fourier series, I think. At any rate, here's what you get with a term with complex numbers in an ...
I think I can at least safely say the following: the spiral interpolator will match (up to the degree of accuracy of the program and computer being used) a...
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Jul 11, 2006 4:03 am
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Here's a way to show angles in 2D. The sectors are colored by 15 degree increments, but this can be changed, as can the sector radius (via the S_r constant). ...
I'm exploring ways to draw sets of related triangles. Here, the blue triangle is a rotated version of the red triangle, and the green triangle is rotated...
Does a reasonably comprehensive list of commands, shortcuts, syntax, etc exist? I have had trouble finding some things, and don't know how complete the list in...
I am trying to make a little Fourier series file that would allow me to type in any old function I please and work out the series to some number of terms. The...
Hello, I have been an avid fan of GC since finding 1.0 on my Power PC twelve years ago; I am a mathematician working at the Univ of Arkansas. We (finally!)...
... The problem seems to be that GC doesn't seem to handle function calls within an integral, unfortunately. Substituting the actual function in seems to work:...
... Just some refresher notes form the "Help" file: I was hoping to Fourier-analyze a step function but unfortunately GC wouldn't evaluate the integral....
On second thought, maybe having the original function in black is clearer here. Then maybe it comes across better that the dotted red-and-green curve is the...
... Now that I look through the help, it's pretty difficult to find a reference on the commands. For example, doing a search for "Calculate" didn't turn up...
... A lot of interesting files here, thanks very much! It takes a while to check them out, of course. Just a few comments on the ones I've had time to check...
Trying to relate Plücker coordinates to models of the real projective plane. http://www.flipcode.com/articles/pluecker_part01.shtml has some amazing graphics...
This is based on the "Boys' Surface" file from the "Examples" menu in the "3. Three dimensions" sub-menu. I'm using solid lines to track the u parameter and...
