Comparison triangle
Define as the 2-dimensional metric space of constant curvature
. So, for example,
is the Euclidean plane,
is the surface of the unit sphere, and
is the hyperbolic plane.
Let be a metric space. Let
be a triangle in
, with vertices
,
and
. A comparison triangle
in
for
is a triangle in
with vertices
,
and
such that
,
and
.
Such a triangle is unique up to isometry.
The interior angle of at
is called the comparison angle between
and
at
. This is well-defined provided
and
are both distinct from
.
References
- M Bridson & A Haefliger - Metric Spaces Of Non-Positive Curvature, ISBN 3-540-64324-9
This article is issued from Wikipedia - version of the 2/17/2011. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.