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Pythagorean
orthogonality of compact sets
Pallavi Aggarwal, Steven Schlicker and Ryan Swartzentruber
Vol. 11 (2018), No. 5, 735–752
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Abstract |
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The Hausdorff metric is used to define the distance between two elements of , the hyperspace of all nonempty compact subsets of . The geometry this metric imposes on 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 , with a focus on attempting to find well-defined notions of angle and angle measure in . |
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Keywords
Hausdorff metric, Pythagorean orthogonality, Pythagorean
triples
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Mathematical Subject Classification 2010
Primary: 51FXX
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Milestones
Received: 17 September 2015
Revised: 2 March 2017
Accepted: 3 December 2017
Published: 2 April 2018
Communicated by Kenneth S. Berenhaut
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Authors |
| Pallavi Aggarwal | |
| California Institute of
Technology Pasadena, CA United States |
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| Steven Schlicker | |
| Department of Mathematics Grand Valley State University Allendale, MI United States |
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| Ryan Swartzentruber | |
| Eastern Mennonite University Harrisonburg, VA United States |
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