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In several high school treatments of geometry, the term "exterior angle theorem" has been applied to a different result, [1] namely the portion of Proposition 1.32 which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. This result, which depends upon Euclid's parallel ...
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34] The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees, and indeed, this is true for any convex polygon, no matter ...
Angle bisector theorem (Euclidean geometry) Ankeny–Artin–Chowla theorem (number theory) Anne's theorem ; Apéry's theorem (number theory) Apollonius's theorem (plane geometry) Appell–Humbert theorem (complex manifold) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis)
Desargues' theorem; Droz-Farny line theorem; Encyclopedia of Triangle Centers; Equal incircles theorem; Equal parallelians point; Equidissection; Equilateral triangle; Euler's line; Euler's theorem in geometry; Erdős–Mordell inequality; Exeter point; Exterior angle theorem; Fagnano's problem; Fermat point; Fermat's right triangle theorem ...
It is uncertain who actually discovered the theorem; however, the oldest extant exposition appears in Spherics by Menelaus. In this book, the plane version of the theorem is used as a lemma to prove a spherical version of the theorem. [8] In Almagest, Ptolemy applies the theorem on a number of problems in spherical astronomy. [9]
Quadratrix compass Angle trisection. The trisection of an arbitrary angle using only ruler and compasses is impossible. However, if the quadratrix is allowed as an additional tool, it is possible to divide an arbitrary angle into equal segments and hence a trisection (=) becomes possible.
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem [1] posed by the 15th-century German mathematician Johannes Müller [2] (also known as Regiomontanus). The problem is as follows: The two dots at eye level are possible locations of the viewer's eye. A painting hangs from a wall.
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