2010, pp 413-433
Date: 23 Aug 2010

Constructions with Straightedge and Compass

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Abstract

The usual meaning of the term construction throughout the history of Geometry, is to draw a figure, usually in the plane, such that the figure possesses certain properties specified a priori. In doing so one is required to start out from a given set of points, in some cases also certain fixed curves. This is referred to as the start data for the construction. One is required to use only certain tools, which have been specified as allowable, and to use them in certain prescribed ways only. Normally one is allowed only a finite number of steps in the construction. If an infinite number of steps is needed, then we speak of an asymptotic version of the construction. To carry out such an asymptotic construction is, of course, not humanly possible. But the method may be used to create constructions which approximate the required one arbitrarily well.