Geodesic
Some Theorems on Convex Polygons
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 329-340

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In this paper diagonals of various orders in a (strict) convex polygon P n are considered. The sums of lengths of diagonals of the same order are studied. A relationship between the number of consecutive diagonals which do not intersect a given maximal diagonal and lie on one side of it and the order of the smallest diagonal among them is established. Finally a new proof of a conjecture of P. Erdos, considered already in [1], is given. 
Altman, E. Some Theorems on Convex Polygons. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 329-340. doi: 10.4153/CMB-1972-060-0
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     title = {Some {Theorems} on {Convex} {Polygons}},
     journal = {Canadian mathematical bulletin},
     pages = {329--340},
     year = {1972},
     volume = {15},
     number = {3},
     doi = {10.4153/CMB-1972-060-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-060-0/}
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