School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type


Publication Date



In this note we introduce a pseudometric on convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a short proof of the theorem by Pinchasi that the sum of perimeters of k convex planar bodies with disjoint interiors contained in a convex body of perimeter p and diameter d is not greater than p+2(k−1)d.

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.