On geodesic triangles with right angles in a dually flat space
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The dualistic structure of statistical manifolds yields eight types of geodesic triangles defining overall eighteen interior angles. In general, the interior angles of geodesic triangles can sum up to π like in Euclidean/Mahalanobis geometry, or exhibit either angle excesses or angle defects. In this paper, we initiate the study of geodesic triangles in dually flat spaces where a generalized Pythagorean theorem holds. First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles. Then we report a construction of triples of points for which the dual Pythagorean theorems hold simultaneously at a point, yielding two dual pairs of dual geodesic triangles with doubly right angles.
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