Loci, 2008
Generalized Baseball Curves: Three Symmetries and You're In! Allison, Diaz, and Miller

• Mathworld has definitions for several generalized baseball curves: great circles, a physical baseball cover, Seiffert's Spherical Spiral, and Viviani's Curve.
• You can find models and animations of Spherical Cycloids and Involutes in the Kinetic Models for Design Digital Library. Spherical cycloids created by cones rolling on other cones are almost generalized baseball curves. They have all the right symmetries, but are not smooth.
• The Skinny on Sewing up Baseballs gives a discussion of how real baseballs are sewn up at .
• The article Exact Cone-Beam Image Reconstruction discusses how a baseball seam orbit enters into the mathematics of cone (x-ray) beam reconstruction using Radon transforms.
• The article Baseball Seam discusses designing a baseball seam using Turbocad.
• The article Pitching Science discusses the role of the seam of the baseball in creating a curve ball pitch. It appears that the seam plays a crucial role in allowing pitchers to pitch a curve ball.
• The Kappa Tau site gives more information on Rudy Rucker's candidate baseball curve ; note, however, that his curve isn't actually quite spherical.
• Gary Helzer's homepage at the University of Maryland contains an article in the form of a Mathematica notebook on Planar Curves with periodic curvature. There's a lot of interesting stuff here; the parts of our above above mathematica notebook that graph planar curves with a specified curvature are taken from here.
• You can download the program 3D-Xploremath for free. This program lets you view many interesting mathematical objects, including several spherical curves, and includes good explainations of each of them.

### References

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