Verging Using a Marked Ruler

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Verging (or insertion) is a characteristic use of a moving marked ruler. Given a point and two straight lines and , verging through with respect to and determines two points and that are one unit apart and such that is on a straight line through and , with on and on . By use of verging, geometric constructions beyond those allowed by the Euclidean straightedge and compass can be carried out. For example, trisection of an angle.

Contributed by: Izidor Hafner (September 2017)
Open content licensed under CC BY-NC-SA


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Details

Verging through the point with respect to the lines with equations and gives coordinates of in terms of , and as the roots of a fourth-degree polynomial.

This Demonstration is based on [1, pp. 124, 125].

Reference

[1] G. E. Martin, Geometric Constructions, NewYork: Springer, 1998.



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