On Sat, Dec 11, 2010 at 7:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
(Simple stuff I couldn't visualize w/o plotting.) Rotate a unit cube about a major diagonal. Its intersection with a plane containing that diagonal varies (with period pi/3) between a rhombus (of side rt(5)/2) and a 1 by rt2 rectangle. --rwg
Forgot to add: It's always a parallelogram. See http://gosper.org/cubewedges.pdf for the rotating cube dodecasected into congruent tetrahedra by the plane, showing that the (in fact nonexistent) azimuthal dependence of the center of oscillation of a cube swung by a corner would be tiny at most. (The larger faces are halves of the aforementioned rectangles and rhombi. Note seeming pi/3 symmetry is really 2pi/3.) --rwg
Who might be able to tell me that "my" Fourier expansion of Jacobi am is a) Centuries old, or b) Just what we've been looking for. ?
The obvious place was dlmf, but their "Fourier" series wasn't real and was inapplicable for the pendulum (m>1, K(m) imaginary case.)