Comparison Triangle

(Metric Geometry)

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Metric Geometry
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What is 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 .

Technology Types

metric geometry

Synonyms

Comparison angle

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 — Date merged: 11/6/2021, 1:32:52 PM
 — Date scraped: 5/20/2021, 5:54:14 PM