Regular polygons?

[wy125]

twanvl:

Are you asking if the maximum area/circumference ratio for an n-sided polygon is achieved when it is a regular polygon? That's how I understood your question.

Why don't you post what you have so far so that we can look at it? You can take the derivative of a sum, just proceed as usual.

I would think that you would need an expression for the Area and circumference for an n-sided polygon (an irregular polygon not a regular one). Divide one by the other, and then take the complete differential. Set each of the partial derivatives to zero and solve the set of equations (there should be n variables I think). The equations will be nonlinear so they might be a little tricky.

You might want to try to look at a triangle first before doing the general case of an n-sided polygon.