This article shows how to construct a tennis ball curve from four circles (scroll down a little to see it): http://www.qedcat.com/archive/165.html I think the four points where the circles meet are required, but that the arcs that connect them can be altered, either exaggerating or reducing their size. Tom rkg writes:
Dear funsters, A tennis-ball appears to be made from 2 congruent pieces of material, seamed together in a curve. Are possible equations to the curve known? I'd like a smooth algebraic equation, probably of degree 4, and preferably with a maximum number of rational points on it. A first approximation might be to take a sphere of radius root(3) and centre at (0,0,0) and take the 8 great circle arcs (1,1,1) to (-1,1,1) to (-1,-1,1), (1,-1,1), (1,-1,-1), (-1,-1,-1), (-1,1,-1), (1,1,-1) and back to (1,1,1). However, this isn't smooth at the 8 corners of the cube, and I think that it doesn't even partition the sphere into two congruent pieces.
Is this well-known to those who well know it? What do the tennis-ball manufacturers do? R.
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