14. Links and references

Other links of interest

• 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

1. D. Allison, R. Diaz, and N. Miller. Generalized baseball curves: An analytic perspective. In preparation, n.d.
2. N. V. Efimov. Nekotorye zadachi iz teorii prostranstvennykh. Usp. Mat. Nauk, 2: 193-194, 1947.
3. P. Erdös. Spiraling the earth with C. G. Jacobi. Am. J. Phys., 68 (10): 888-895, 2000.
4. W. Fenchel. The differential geometry of closed space curves. Bull. Amer. Math. Soc., 57: 44-45, 1951.
5. A. Gray. Modern Differential Geometry of Curves and Surfaces with Mathematica. CRC Press, Boca Raton, second edition, 1998.
6. D. Henderson. Differential Geometry: A Geometric Introduction. Prentice-Hall, New Jersey, 1998.
7. D. Henderson and D. Taimina. Experiencing Geometry: Euclidean and Non-Euclidean With History. Prentice-Hall, New Jersey, 3rd edition, 2005.
8. M. Hirsch, S. Smale, and R. Devaney. Differential Equations, Dynamical Systems, and An Introduction to Chaos. Elsevier, San Diego, CA, second edition, 2004.
9. C.-C. Hwang. A differential geometric criterion for a space curve to be closed. Proc. Amer. Math. Soc., 83: 357-361, 1981.
10. F. López-López. Question #48. Is there a physical property that determines the curve that defines the seam of a baseball? American Journal of Physics, 64 (9): 1097, 1996.
11. R. Millman and G. Parker. Elements of Differential Geometry. Prentice-Hall, New Jersey, 1977.
12. Y. Nikolaevsky. On Fenchel's problem. Mathematical Notes, 56: 87-89, 1994.
13. P. Scofield. Curves of constant precession. Amer. Math. Monthly, 102 (6): 531-537, 1995.
14. R. Thompson. Designing a baseball cover. College Mathematics Journal, 29 (1): 48-61, 1998.
15. D. von Seggern. Practical Handbook of Curve Design and Generation. CRC Press, Boca Raton, FL, 1994.
16. E. W. Weisstein. Baseball cover, n.d. From MathWorld-A Wolfram Web Resource.