I'd always casually assumed that the tennis-ball / baseball curve was probably some simple space quartic that everybody but me knew about. But since it seems this is not the case, I'll put in my two-penn'orth. The classic minimal Enneper's surface intersects concentric spheres in a family of such curves. With the parameterisation in the Wikipedia page, a sphere of small radius meets it in an approximate circle; a sphere of radius (approx?) 1/4 meets it in a typical tennis-ball curve, with expected symmetry and arcs parallel at the extremities; a sphere of radius (approx?) 1 meets it in a curve with touching arcs; for larger radius the curve has 4 self-intersections. See http://www.indiana.edu/~minimal/maze/enneper.html http://en.wikipedia.org/wiki/Enneper_surface The degree of Enneper's surface equals 9, so presumably these curves have degree 18. Fred Lunnon On 11/3/13, Henry Baker <hbaker1@pipeline.com> wrote:
Is a tennis ball seam the same shape as a baseball seam?
http://math.arizona.edu/~rbt/baseball.PDF
"Designing a Baseball Cover"
Richard B. Thompson
College Mathematics Journal, Jan. 1998.
At 09:09 AM 11/3/2013, rkg wrote:
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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