given two triangles
21Triangle group — In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle.… …
22Music theory — is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers techniques across or within genres, styles, or historical periods. In a grand sense, music theory distills… …
23Fermat point — In geometry, the first Fermat point, or simply the Fermat point, also called Torricelli point, is the solution to the problem of finding a point F inside a triangle ABC such that the total distance from the three vertices to point F is the… …
24Rational trigonometry — is a recently introduced approach to trigonometry that eschews all transcendental functions (such as sine and cosine) and all proportional measurements of angles. In place of angles, it characterizes the separation between lines by a quantity… …
25Hexagram — For symbols used in the I Ching, see Hexagram (I Ching) : For a Jewish symbol, see Star of David. : For Occultic symbol see Unicursal hexagram A hexagram is a six pointed geometric star figure, {6/2} or 2{3}, the compound of two equilateral… …
26Desargues' theorem — Perspective triangles. Corresponding sides of the triangles, when extended, meet at points on a line called the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of… …
27Archimedes — For other uses, see Archimedes (disambiguation). Archimedes of Syracuse (Greek: Ἀρχιμήδης) …
28Hilbert's axioms — are a set of 20 assumptions (originally 21), David Hilbert proposed in 1899 as the foundation for a modern treatment of Euclidean geometry. Other well known modern axiomatizations of Euclidean geometry are those of Tarski and of George… …
29Heronian triangle — In geometry, a Heronian triangle is a triangle whose sidelengths and area are all rational numbers. It is named after Hero of Alexandria.PropertiesAny triangle whose sidelengths are a Pythagorean triple is Heronian, as the sidelengths of such a… …
30Invariant (mathematics) — In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually… …
