Topic: From the triangle inequality to the isoperimetric inequality



Abstract:  Starting from the fact that the sum of the lengths of two sides of 

a triangle is greater than that of the third side, we will study a
series of shape optimization problems for polygons and, finally,
deduce the classical isoperimetric inequality in the plane. The talk
will be accessible to those with a familiarity with plane geometry
(triangles) and elementary notions of analysis like `supremum,' `limits' and `continuity'.