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An Extremal Problem for Polygons Inscribed in a Convex Curve

Published online by Cambridge University Press:  20 November 2018

Béla Bollobás
Béla Bollobás*
Affiliation:
L. Eötvös University, Budapest
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A. Zirakzadeh (1) has determined for n = 3 the minimal value of the perimeter length of a polygon A1 A2 … An, where A1, A2, … , An–1, and An divide the perimeter of a convex curve C, of perimeter length l, into n parts of equal length; further he has stated a conjecture concerning the general case. In the following a simpler proof for the case n = 3 is given; the minimum for even values of n, which confirms the conjecture of A. Zirakzadeh, is determined; and a fairly precise estimation for odd values of n, which refutes the conjecture of A. Zirakzadeh, is given. For n = 3 we have the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 523 - 528
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Zirakzadeh, A., A property of a triangle inscribed in a convex curve, Can. J. Math, 16 (1964), 777–786.Google Scholar