On fencing problems |
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Authors: | C Miori C Peri S Segura Gomis |
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Institution: | aDepartamento de Análisis Matemático, Universidad de Alicante, E-03080 Alicante, Spain;bUniversità Cattolica S.C., Largo Gemelli 1, I-20123 Milano, Italy |
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Abstract: | Fencing problems regard the bisection of a convex body in a way that some geometric measures are optimized. We introduce the notion of relative diameter and study bisections of centrally symmetric planar convex bodies, bisections by straight line cuts in general planar convex bodies and also bisections by hyperplane cuts for convex bodies in higher dimensions. In the planar case we obtain the best possible lower bound for the ratio between the relative diameter and the area. |
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Keywords: | Fencing problems Optimization Relative diameter |
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