A mechanical device for trisecting an angle called the tomahawk appeared in a book in 1835...

A mechanical device for trisecting an angle called the tomahawk appeared in a book in 1835 (its inventor is unknown). It may be constructed and tested efficiently using Sketchpad.

[1] Construct point R and translate it horizontally 0.75 units (inches) three times, to obtain points S, T, and U, equally spaced. Construct segment

[2] Construct the perpendicular bisector of segment at S, locate a point V on it, then hide the line and construct segment

[3] With T as center, construct a semicircle with diameter as base. (Use Construct Arc on Circle technique.)

[4] (Optional) If desired, fill in with shading using Polygon Interior and Arc Segment Interior under CONSTRUCT—inessential to the function of the Tomahawk as a trisector.

(a) test this device, construct by rotation, an angle ∠ABC having measure 60— an angle that cannot be trisected with the Euclidean tools. Using the Translate Tool and by dragging one point of the ray position the angle so that B lies on ray passes through R, and ray is tangent to the semicircle. Construct segments and These will be the angle trisectors. Measure the angles ∠RBS, ∠SBT, and ∠TBC to check.

(b)Does this instrument seem to work? Why? Try to prove its validity. (We are in Euclidean geometry now.)