| Abstract: | Optimization, a principle of nature and engineering design, in real life problems is normally achieved by using numerical
methods. In this article we concentrate on some optimization problems in elementary geometry and Newtonian mechanics. These
include Heron’s problem, Fermat’s principle, Brachistochrone problems, Fagano’s problem, geodesics on the surface of a parallelepiped,
Fermat/Steiner problem, Kakeya problem and the isoperimetric problem. Some of these are very old and historically famous problems,
a few of which are still unresolved. Close connection between Euclidean geometry and Newtonian mechanics is revealed by the
methods used to solve some of these problems. Examples are included to show how some problems of analysis or algebra can be
solved by using the results of these geometrical optimization problems. |
