When viewed from above, 1 5 2 6 3 7 4 8 looks much more evenly distributed than 1 2 3 4 5 6 7 8. Here's a sketch in GeoGebra that shows it: https://www.geogebra.org/3d/j2tbpftt. You can change the numbers in the variable 'sizes' to rearrange the wires. If you try to maximise the sum of differences between adjacent wires, your and Drew's whisks do quite well but 1 5 2 7 3 8 4 6, and 11 other arrangements, do slightly better. On Mon, 29 Oct 2018 at 02:06 James Propp <jamespropp@gmail.com> wrote:
My 8-wire balloon whisk has wires that, read clockwise, follow the pattern 1 5 2 6 3 7 4 8, where 1 stands for the shortest wire, 2 stands for the second-shortest wire, etc. But Drew Lewis has an 8-wire whisk that goes 1 5 8 4 6 2 7 3. (He also has a 1 6 2 7 3 8 4 9 5 10 and a 1 4 2 5 3 and a 1 3 2, and I have a 1 2 3 4.)
Is there any rhyme or reason (or math!) behind this diversity?
(I personally would like to have a 1 5 3 7 2 6 4 8 whisk, since I’m a fan of the van der Corput sequence.)
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun