higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
Trigonometry is a geometric discipline which comprises the study of metric properties of triangles (measures of angles, sides and of various auxiliary segments and angles constructed from given triangle), usually on a euclidean or hyperbolic plane or on a unit sphere. Thus we distinguish the usual euclidean from spherical and hyperbolic trigonometry; there are also generalizations to trigonometry over other fields.
Trigonometric functions for real values of argument can be defined in terms of trigonometry of unit triangle (triangle with one of the sides of unit length), where the argument is understood as an angle whose longer side is of unit length. Similarly for hyperbolic trigonometric functions which can be geometrically defined in terms of hyperbolic unit triangles.
Norman Wildberger, Universal hyperbolic geometry I: trigonometry, Geometriae Dedicata 163(1), 2009 arxiv/0909.1377 doi
wikipedia: trigonometry, spherical trigonometry
Last revised on May 10, 2019 at 15:10:10. See the history of this page for a list of all contributions to it.