Verging Using a Marked Ruler

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.


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