A set in
is called
-convex if, for any two distinct points in
, there exists a third point in
, such that one of the three points is equidistant from the others. In this paper we first investigate nondiscrete
-convex sets, then discuss about the
-convexity of the eleven Archimedean tilings, and treat subsequently finite subsets of the square lattice. Finally, we obtain a lower bound on the number of isosceles triples contained in an
-point
-convex set.
Isosceles triple convexity
Yuang, Liping, Zamfirescu, Tudor and Zhang, Yue
Abstract

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Additional Information
Author(s) | Yuan, Liping, Zamfirescu, Tudor, Zhang, Yue |
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DOI | https://doi.org/10.37193/CJM.2017.01.13 |