[math-fun] Mildly surprising: The 2-sphere of radius 2
(at the origin) bisects the unit 2-sphere at (1,1,1): Graphics3D[{Sphere[{0, 0, 0}, 2], Sphere[{1, 1, 1}]}, PlotRange -> {{0, 2}, {0, 2}, {0, 2}}] gosper.org/2spheres.png --rwg
Nice! On Mon, Jul 14, 2014 at 10:59 AM, Bill Gosper <billgosper@gmail.com> wrote:
(at the origin) bisects the unit 2-sphere at (1,1,1): Graphics3D[{Sphere[{0, 0, 0}, 2], Sphere[{1, 1, 1}]}, PlotRange -> {{0, 2}, {0, 2}, {0, 2}}] gosper.org/2spheres.png --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Are there other examples of integer-radius, integer-centered spheres (of arbitrary dimension) dissecting each other in integer ratios? On Mon, Jul 14, 2014 at 2:06 PM, Tom Rokicki <rokicki@gmail.com> wrote:
Nice!
On Mon, Jul 14, 2014 at 10:59 AM, Bill Gosper <billgosper@gmail.com> wrote:
(at the origin) bisects the unit 2-sphere at (1,1,1): Graphics3D[{Sphere[{0, 0, 0}, 2], Sphere[{1, 1, 1}]}, PlotRange -> {{0, 2}, {0, 2}, {0, 2}}] gosper.org/2spheres.png --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (3)
-
Allan Wechsler -
Bill Gosper -
Tom Rokicki