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Construction of a regular pentagon. In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not.
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass.
The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P that are parallel to L. [1] As in Euclidean geometry, where ancient Greek mathematicians used a compass and idealized ruler for constructions of lengths, angles, and other geometric figures ...
Martin originally intended his book to be a graduate-level textbook for students planning to become mathematics teachers. [2] However, as well as this use, it can also be read by anyone who is interested in the history of geometry and has an undergraduate-level background in abstract algebra, or used as a reference work on the topic of geometric constructions.
Trisection can be approximated by repetition of the compass and straightedge method for bisecting an angle. The geometric series 1 / 3 = 1 / 4 + 1 / 16 + 1 / 64 + 1 / 256 + ⋯ or 1 / 3 = 1 / 2 − 1 / 4 + 1 / 8 − 1 / 16 + ⋯ can be used as a basis for the ...
Cover of Lemoine's "Géométrographie" In the mathematical field of geometry, geometrography is the study of geometrical constructions. [1] The concepts and methods of geometrography were first expounded by Émile Lemoine (1840–1912), a French civil engineer and a mathematician, in a meeting of the French Association for the Advancement of the Sciences held at Oran in 1888.
Neusis construction. In geometry, the neusis (νεῦσις; from Ancient Greek νεύειν (neuein) 'incline towards'; plural: νεύσεις, neuseis) is a geometric construction method that was used in antiquity by Greek mathematicians.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
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