Document Type


Source Publication Title

Technical Report 351


The ancient Greek mathematician Heron was the first to solve the problem of finding the shortest path from point A to point B on one side of the line L, subject to the condition that the path goes from A to L and then to B (figure 1). Figure 1. His solution involved going from A to point R on L and then to B such that the line segments AR and BR make equal angles with L. This is exactly the path a light ray from A to B if L were a mirror. Heron included this proposition in his book Catoptrica, theory of mirrors. See Kline [5], p.168. We use the method of Lagrange multipliers to extend Heron's problem from the Euclidean plane to real normed linear planes where the unit circles of the norm are strictly convex and are continuously differentiable. We also generalize familiar results from Euclidean geometry on the reflection properties of conics. In this introductory section we briefly review some results from Euclidean geometry and some basic properties of a norm which we will use in the following sections.


Mathematics | Physical Sciences and Mathematics

Publication Date




Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.