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The first construction is due to Erchinger, a few years after Gauss's work. The first explicit constructions of a regular 257-gon were given by Magnus Georg Paucker (1822) [5] and Friedrich Julius Richelot (1832). [6] A construction for a regular 65537-gon was first given by Johann Gustav Hermes (1894). The construction is very complex; Hermes ...
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 pair of compasses.
Geometric Constructions is a mathematics textbook on constructible numbers, and more generally on using abstract algebra to model the sets of points that can be created through certain types of geometric construction, and using Galois theory to prove limits on the constructions that can be performed.
The next construction is originally due to Archimedes, called a Neusis construction, i.e., that uses tools other than an un-marked straightedge. The diagrams we use show this construction for an acute angle, but it indeed works for any angle up to 180 degrees. This requires three facts from geometry (at right):
The Ancient Tradition of Geometric Problems studies the three classical problems of circle-squaring, cube-doubling, and angle trisection throughout the history of Greek mathematics, [1] [2] also considering several other problems studied by the Greeks in which a geometric object with certain properties is to be constructed, in many cases through transformations to other construction problems. [2]
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.