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| Currently, the prize for Megamillions is over a billion dollars. Pick 5 numbers from 1 to 70, then pick one number from 1 to 25. Odds of winning Megamillions: 25 Binomial[70, 5] = 302575350 Not sure what the odds are of just one... |
| &[Wolfram Notebook][1] I'd be curious if anyone can find more perfect series dissections. [1]: https://www.wolframcloud.com/obj/82f03a84-4159-408d-9ba8-52bdef8cd000 |
| Do you have a picture of the graph you want labeled? In general, no. It's still unsolved if all trees can be gracefully labeled. |
| Here's the "simpler" form that might work with the rhombic dodecahedron: points = {{0, 0, 0}, {12, 0, 0}, {0, 0, 12}, {0, 12, 0}, {3, 3, -3}, {3, -3, 3}, {-3, 3, 3}, {9, 9, 3}, {9, 3, 9}, {3, 9, 9}, {8, 8, 8}}/6; ConvexHullMesh[points] ... |
| This looks very nice. A slightly simpler demo might show 1. Trilinear coordinates 2. Barycentric coordinates |
| Another trick Brillhart = {{0, 2, 2}, {1, 0, 2}, {2, 1, 0}}; bc = Eigenvalues[Brillhart][[1]]; N[Log[(2 + bc)^24 - 24]/Sqrt[163], 34] 3.141592653589793238462643383279503 N[Pi, 34] 3.141592653589793238462643383279503 |
| Well, I took a look at the wild example, then took a wild guess that the following would be perfect: dat = FoldList[PolyhedronFaceReflect, a4, {3, 2, 5, 3, 2, 5, 2, 1, 2, 5, 2, 3, 5, 2, 3, 2, 1}]; Graphics3D[{{Red, Sphere[v[[6]]... |
| &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/04583976-5a80-43c2-9cd2-a9df6e976d2d |
| What polynomial needs to solved to brace the 17-gon? We could argue that the 7-gon doesn't have a direct side to side bracing because that triangle of braces would imply the 7-gon (or 9-gon) is constructible. |
| Murray, The code in this demo requires version 12.3. However, that version of the CDF isn't yet incorporated into the Demonstrations build system. Once that is ready, I plan to republish with the CDF. I didn't want to make the author wait longer... |