LOWER BOUND OF LENGTH OF TRIANGLE INSCRIBED IN A CIRCLE ON NON-EUCLIDEAN SPACES

• Journal title : Honam Mathematical Journal
• Volume 34, Issue 1,  2012, pp.103-111
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2012.34.1.103
Title & Authors
LOWER BOUND OF LENGTH OF TRIANGLE INSCRIBED IN A CIRCLE ON NON-EUCLIDEAN SPACES
Chai, Y.D.; Lee, Young-Soo;

Abstract
Wetzel[5] proved if $\small{{\Gamma}}$ is a closed curve of length L in $\small{E^n}$, then $\small{{\Gamma}}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.
Keywords
circle;diameter;hyperbolic plane;minimum chord;spherical geometry;
Language
English
Cited by
References
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