Electronic Resource
Springer
Archiv der Mathematik
74 (2000), S. 75-80
ISSN:
1420-8938
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. In this paper we consider the problem of finding the n-sided ( $n\geq 3$ ) polygons of diameter 1 which have the largest possible width w n . We prove that $w_4=w_3= {\sqrt 3 \over 2}$ and, in general, $w_n \leq \cos {\pi \over 2n}$ . Equality holds if n has an odd divisor greater than 1 and in this case a polygon $\cal P$ is extremal if and only if it has equal sides and it is inscribed in a Reuleaux polygon of constant width 1, such that the vertices of the Reuleaux polygon are also vertices of $\cal P$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00000413
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