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The sum of the internal angle and the external angle on the same vertex is π radians (180°). The sum of all the internal angles of a simple polygon is π (n −2) radians or 180 (n –2) degrees, where n is the number of sides. The formula can be proved by using mathematical induction: starting with a triangle, for which the angle sum is 180 ...
Hinge theorem. In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the ...
In geometry, two triangles are said to be orthologic if the perpendiculars from the vertices of one of them to the corresponding sides of the other are concurrent (i.e., they intersect at a single point ). This is a symmetric property; that is, if the perpendiculars from the vertices A, B, C of triangle ABC to the sides EF, FD, DE of triangle ...
The hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. [1] The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths, The reciprocal lattice of the hexagonal lattice is a ...
Apex (geometry) In geometry, an apex (pl.: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some "base". The word is derived from the Latin for 'summit, peak, tip, top, extreme end'. The term apex may used in different contexts:
Wikipedia's contents: Mathematics and logic. edit · watch. Mathematics is the study of topics such as quantity (numbers), structure, space, and change. It evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects.
Triangulation (geometry) In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together. In most instances, the triangles of a ...
A trifecta of bearish factors could send stocks lower by about 10% within the next few weeks, according to Renaissance Macro Research founder and technical strategist Jeff DeGraaf. In an interview ...
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