Special_Tools for Angle Trisection

Go to Fun_Math Content Table Trisecting an Angle Special Tools

Trisection using Special Tools

"Tomahawk"

"Tomahawk" is shown in the figure shown below.

Tomahawk is made up of straight edge OQ, a semicircle SQR, and a sharp corner point "P" at a distance of the same radius from point "Q". The angle to be trisected is AOB.

The trisection is done when the point "P" passes through line AO while the inside edge OQ of the Tomahawk's handle being kept on the point "O". Just as in the case of Carpenter's Square, the following relation holds.

PQ = QS = SR

You can see the process in animation.

******** tomahawk_desc.dwg ********

Actual Model Example

The Carpenter's Square in the author's garage was used in the actual test for trisecting 60 degrees angle. (shown in the left of the following picture.)

This ruler has different width for two legs, 1.0 and 1.5 inch.

Shown in the right is a copy of this ruler made of a transparent,film-like vinyl sheet used as separater in the binder.
******** tomahawk_example_2.dwg ********

To create this drawing and animation:
   Load     tomahawk_3.lsp    (load "tomahawk_3")
  Then from command line, type   tomahawk
  For a quick look , type   test & detail_test

Animation file creation: animation_tomahawk

Example Run: 60 degrees case:

******** tomahawk_60_deg_case.dwg ********

References

1. Yates,Robert Carl : "The Trisection problem", p 37

Go to Fun_Math Content Table Trisecting an Angle Special Tools

All questions/suggestions should be sent to Takaya Iwamoto

Last Updated Nov 22, 2006