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2018 Pythagorean orthogonality of compact sets
Pallavi Aggarwal, Steven Schlicker, Ryan Swartzentruber
Involve 11(5): 735-752 (2018). DOI: 10.2140/involve.2018.11.735

Abstract

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).

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Pallavi Aggarwal. Steven Schlicker. Ryan Swartzentruber. "Pythagorean orthogonality of compact sets." Involve 11 (5) 735 - 752, 2018. https://doi.org/10.2140/involve.2018.11.735

Information

Received: 17 September 2015; Revised: 2 March 2017; Accepted: 3 December 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06866580
MathSciNet: MR3784023
Digital Object Identifier: 10.2140/involve.2018.11.735

Subjects:
Primary: 51Fxx

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2018
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