Abstract
A spherical ball obviously has the property that it can be arbitrarily rotated between two fixed parallel planes without losing contact with either plane. It has been known for a long time, certainly since the time of Euler, that there are other convex bodies with the same property. Such bodies are called convex bodies of constant width. Other names that have also been used are ‘convex bodies of constant breadth’, ‘equiwide convex bodies’, ‘orbiforms’ and ‘spheroforms’ (in the two and three-dimensional case, respectively) and several more; the occasionally used German ‘Gleichdick’ being one of the most charming.
Supported by National Science Foundation research grant MCS-8001578
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Chakerian, G.D., Groemer, H. (1983). Convex Bodies of Constant Width. In: Gruber, P.M., Wills, J.M. (eds) Convexity and Its Applications. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5858-8_3
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