A theorem is proposed
for the areas of n-sided convex polygons, of given lengths of sides. The
theorem is illustrated as a simple but powerful one in estimating the areas
of irregular polygons, being dependent only on the number of sides n (and not
on any of the specific angles) of the irregular
polygon. Finally, because of the global symmetry shown by equilateral
triangles, squares and circles
under group (gauge) theory, the relationships govering this areas, when their are inscribed
or escribed in one another are discussed as riders, and some areas of their applications in graph
theory, ratios and maxima and minima
problems of differential calculus
briefly mentioned
|