When Four Cyclic Antipodal Points Are Ordered Counterclockwise in Euclidean and Hyperbolic Geometry
Abraham A. Ungar
Abstract:A cyclic antipodal points of a circle is a pair of
points that are the intersection of the circle with a diameter
of the circle. A recent proof of Ptolemy’s Theorem, simultaneously
in both (i) Euclidean geometry; and (ii) the relativistic
model of hyperbolic geometry (which is identified with the
Klein model of hyperbolic geometry), motivates in this article
the study of four cyclic antipodal points of a circle, ordered
arbitrarily counterclockwise. The translation of results from
Euclidean geometry into hyper… Show more
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