Title Page

Abstract

Several authors have tried to give equations describing the curve traced out on the surface of a baseball by its seam. Taking an alternative approach, we identify several symmetry properties that any reasonable candidate for a baseball curve must have and call the class of curves on the sphere that have these symmetries generalized baseball curves. We show that curves whose geodesic curvature functions satisfy certain symmetries are in fact generalized baseball curves as long as they are closed or periodic. We look at the family of curves whose geodesic curvature is of the form sin(cs), and show that there are many such curves that do close back on themselves and are therefore generalized baseball curves. Along the way, we come up with what we think is a nice and previously undiscussed curve that fits the actual seam of a baseball surprisingly well.

Technologies Used in This Article

• This article uses Java (1.4.2 or later) for several interactive applets created with LiveGraphics3D. You may need to install or upgrade the Java plug-in.
• The XML version of the article uses MathML, the Mathematics Markup Language for the display of mathematical expressions. You will need either Mozilla Firefox with the appropriate fonts installed or Internet Explorer with the MathPlayer plug-in.
• The Mathematica notebooks available for download require either Mathematica or the free Mathematica Player.

Publication data

• Published September, 2008
• Copyright © 2008, Dean Allison, Ricardo Diaz, and Nathaniel Miller

Article Link

• Generalized Baseball Curves: Three Symmetries and You're In! (XML)
• Generalized Baseball Curves: Three Symmetries and You're In! (HTML)