[math-fun] MasterCard "football" is too skinny.
Two congruent circles through each other's centers make a biconvex "lens" with 120º arcs. Revolving this around its long axis gives a solid with girth ratio r = 2/3 + 1/√3 ~ 1.244016935856293. Regulation football: 58/43 ≥ r ≥ 280/219 ~ 1.348837209302326 ≥ r ≥ 1.278538812785388. Technically this surface is a geometric torus, although not a topological one. As I reported to at least some of you, Mathematica can only do the area integral numerically. But so accurately that ries quickly expresses it in terms of π and √3. Bisecting the revolved solid on a short axis produces the larger face of an "orbiform" constant diameter balanoid solid. I'm still hoping someone with a Blenderoid physics engine can tell me the approximate "angle of repose" of an orbiform resting on its larger face. --rwg
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Bill Gosper