Titlebook: Bodies of Constant Width; An Introduction to C Horst Martini,Luis Montejano,Déborah Oliveros Textbook 2019 Springer Nature Switzerland AG 2

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Examples and Constructions,ant width is undoubtedly the Reuleaux triangle of width . which is the intersection of three disks of radius . and whose boundary consists of three congruent circular arcs of radius .. In Section ., we will see that the Reuleaux triangle can be generalized to plane convex figures of constant width .

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Sections of Bodies of Constant Width, 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 concl

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https://doi.org/10.1007/b138350rds of a convex body that have maximum length, and it is their behavior which gives constant width bodies their basic properties. Unlike the diameters of a ball, those of a body of constant width do not always meet at a single point, but when they do so, it is because the body is indeed a ball.

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