Optimization Problems in Elementary Geometry

Dr. Asok Kumar Mallik

India Institute of Technology
Kanpur, India

June 21, 2007
202 Madison Hall
3:00 PM (Refreshments at 2:30 in 201 Madison Hall)

Abstract

Optimization is a principle of nature and an index of quality of engineering design. In this talk we shall discuss examples of optimization in elementary geometry. Since Euclidean geometry and Newtonian mechanics are closely related we will see how methods developed in one can be applied to solve problems in the other area. Heron's problem, Fermat's principle, brachitochrone of Bernoulli and Galileo will be followed by Fagano's problem, Fermat/Steiner problem, Geodesics on a parralelopiped, Kakya's problem. At the end, Isoperimetric quotient and its applications will be discussed.