Vol. 11, No. 5, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 183–364
Issue 1, 1–182

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
This article is available for purchase or by subscription. See below.
Pythagorean orthogonality of compact sets

Pallavi Aggarwal, Steven Schlicker and Ryan Swartzentruber

Vol. 11 (2018), No. 5, 735–752

The Hausdorff metric h is used to define the distance between two elements of (n), the hyperspace of all nonempty compact subsets of n. The geometry this metric imposes on (n) is an interesting one — it is filled with unexpected results and fascinating connections to number theory and graph theory. Circles and lines are defined in this geometry to make it an extension of the standard Euclidean geometry. However, the behavior of lines and segments in this extended geometry is much different from that of lines and segments in Euclidean geometry. This paper presents surprising results about rays in the geometry of (n), with a focus on attempting to find well-defined notions of angle and angle measure in (n).

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Hausdorff metric, Pythagorean orthogonality, Pythagorean triples
Mathematical Subject Classification 2010
Primary: 51FXX
Received: 17 September 2015
Revised: 2 March 2017
Accepted: 3 December 2017
Published: 2 April 2018

Communicated by Kenneth S. Berenhaut
Pallavi Aggarwal
California Institute of Technology
Pasadena, CA
United States
Steven Schlicker
Department of Mathematics
Grand Valley State University
Allendale, MI
United States
Ryan Swartzentruber
Eastern Mennonite University
Harrisonburg, VA
United States