Abstract
In Chapter 3 it was proven that the property of constant width is inherited under orthogonal projection but not under sections. The proof of this fact was not a constructive one, that is, no nonconstant width section of a body of constant width was actually exhibited. In fact, it was proven that if all sections of a convex body have constant width, then the body is a ball. Since there are bodies of constant width other than the ball, it was concluded that they must all have at least one section that is not of constant width. To show this could, however, be tricky, even in cases as simple as the body produced by rotating the Reuleaux triangle around one of its axes of symmetry.
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