Geodesic
An Extremal Problem for Polygons Inscribed in a Convex Curve
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 523-528

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Bollobás, Béla. An Extremal Problem for Polygons Inscribed in a Convex Curve. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 523-528. doi: 10.4153/CJM-1967-045-5
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[1] 1. Zirakzadeh, A., A property of a triangle inscribed in a convex curve, Can. J. Math, 16 (1964), 777–786. Google Scholar

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