Triangle center Since rotations and translations may be regarded as double reflections they too must preserve triangle centers. These invariance properties provide justification for the definition. Some other names for dilation are uniform scaling, isotropic scaling, homothety, and homothecy. The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both Euclidean and hyperbolic geometry. In order for the expressions to coincide, the expressions must "not" encapsulate the specification of the angle sum being 180 degrees.
Angles at the centre of the Angle homeland in the northeastern portion of the modern German "Bundesland" of Schleswig-Holstein, on the Jutland Peninsula. There, a small peninsular area is still called Anglia today and is formed as a triangle drawn roughly from modern Flensburg on the Flensburger Fjord to the City of Schleswig and then to Maasholm, on the Schlei inlet. Attribution: Angles The Angles () were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several of the kingdoms of Anglo-Saxon England, and their name is the root of the name England.