ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. In the Euclidean plane, decompose a convex body T into n\geq 2 convex bodies T 1 ,\ldots ,T n with areas also denoted by T 1 ,\ldots ,T n , and with perimeters L 1 ,\ldots ,L n . For T a polygon with at most six sides, G. Fejes Tóth and also L. Fejes Tóth showed that the isoperimetric quotient (L 1 + ⋅s + L n )/(\sqrt T 1 + ⋅s + \sqrt T n ) is greater than the corresponding isoperimetric quotient of a regular hexagon if T i /T j for any i, j is bounded from below by some appropriate constant. We generalize this result to any convex body T , and we show the analogous result for the isoperimetric quotient (L 2 1 + ⋅s + L 2 n )/(T 1 + ⋅s + T n ) .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004540010084
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