MathDB

46

Part of 1969 IMO Shortlist

Problems(1)

Positioning of points to get max and min area.

Source:

10/4/2010
(NET1)(NET 1) The vertices of an (n+1)−(n + 1)-gon are placed on the edges of a regular n−n-gon so that the perimeter of the n−n-gon is divided into equal parts. How does one choose these n+1n + 1 points in order to obtain the (n+1)−(n + 1)-gon with (a)(a) maximal area; (b)(b) minimal area?
geometryperimeterpolygonareaoptimizationIMO ShortlistIMO Longlist