Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 2, pp. 519-529 (2010)
Limits along lines with common ends in Hyperbolic Geometry
D. Ruoff and J. ShilletoDrusbergstr. 17, 8810 Horgen, Switzerland; 3440 Yosemite Ave, El Cerrito, CA, USA 94530
Abstract: Let $P$ be a point outside a pair $a, b$ of boundary parallel lines in the hyperbolic plane, and consider the lengths of the segments that are collinear with $P$ and join $a$ with $b$. The limit length of these segments is determined in a new, elementary way, and the variation of lengths is found using coordinates developed from Hilbert's Arithmetic of Ends.
Classification (MSC2000): 51M09, 51M10
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Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.