View source for Talk:Hexagon

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The maximum [[diameter]] a hexagon can have is twice its side length, and the minimum is <math>s\sqrt{3}</math>.
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The diameter of a set (by definition) is the supremum of the distances between two points of the set.
--[[User:JBL|JBL]] 11:55, 1 November 2006 (EST)

English please? --[[User:I like pie|I_like_pie]] 20:21, 1 November 2006 (EST)

"Supremum" = "least upper bound."  In many situations this just means "maximum," but there are others where it doesn't.  For example, in an open set such as the interior of a circle or radius <math>r</math>, there are no two points at a distance <math>2r</math> from each other, but the diameter of the set is still <math>2r</math>.  Or, if we consider the set <math>\{1, \frac12, \frac13, \ldots\}</math> this set has diameter 1 even though it contains no two points at distance 1 from each other.

The point was just that there is only one value which is the diameter of a given set.  The notion you're trying to capture is something to do with the lengths of paths from points on the hexagon passing through the center, or some such -- it would probably be better just to give the lengths of the apothem and circumradius, instead.