Friday, 19 June 2009

A Mechanical Trisection of theAngle


In the June issue following the Maskelyne trisection article I mentioned, there was a post by J. R. Cotter, that proposed a simple, exact (within mechanical limits) and apparently original trisection device. I have created a geogebra aplet to emulate the method for those who wish to explore.
The idea, shown in the image above is as follows. A mechanical linage with four pens labeled A, B, C, and D is created so that A is fixed at the vertex of the angle, and B is allowed to slide along one ray of the angle. Pens B, C, and D are constrained to a straight line, and the distances AC, BC, AD are all equal. AS B is moved along the ray of the angle, the point D will be moved around the fixed point at A.

When D is aligned with the line along the terminal ray of the angle, the angle ABD is 1/3 of the original angle.
The aplet allows you to change the original angle, and includes construction devices to emulate the mechanical linkage described in the paper and help visualize a proof of the trisection. Enjoy...
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