Euclid Challenge - Trisection Of Any Angle By Straightedge And Compass

Successful Response by Milton Mintz

May 10, 2002

Page 7: Trisection of Any Angle by Straightedge and Compass

Turn the “chart page” 90° to the left, from “portrait” to “ “landscape”.
Grasp with the left hand a compass leg above the legpoint. (Identify as leg R).
Place legpoint of leg R on point D’.
Grasp with the right hand the other compass leg above the legpoint. (Identify as leg S).
Place legpoint of leg S on point D.
Move both legpoints at a uniform rate; legpoint of leg R along arc D’ C’ towards point C’; and legpoint of leg S along arc DC towards point C.
When the legpoint of leg R reaches point P’, stop both legpoints. At the location of the legpoint of leg S on arc DC, mark point T -- Trisection point *.
From point D, on arc AD, length arc DT, mark point T’.
Arc TT’ trisects Angle ABC by straightedge and compass.

* Confirmation of the “Uniform Rate”: The maximum travel on arc D’C’ = 5.625°. (1/8 of 45°) and on arc DC = 7.5° (1/6 of 45° or 1/4 of 30°). These two angles, 5.625° and 7.5° can be constructed with a compass, and used for test points by continuing the movement of the two legpoints beyond the 3 3/4° on arc K’L’, and 5° on arc KL, to see that legpoint R reaches test point 5.625° the same time that legpoint S reaches test point 7.5°

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