Tomahawk angle trisector - photo

[mklotz]

It's a puzzle to me, how the 'rigid' contours operate to bisect angles whether obtuse or acute. I don't see it in drawing near as useful, where all kinds of geometry can do this. That said, in duplication, it would be on material (sheet metal, wood), or a completed object, that presents unwieldy size

Go to the Wikipedia article on the tomahawk...

https://en.wikipedia.org/wiki/Tomahawk_(geometry)

and page down to the "Trisection" portion. That will show you how the tool geometry is exploited to trisect angles.

In Euclidian geometry there was a strong concentration on using only a compass and (uncalibrated) straightedge to solve various geometric problems. Since bisection was easy with these tools, it was expected that trisection should be possible. Only later was it proved that trisection with those tools was impossible.

All these attempts led to an interest in trisection and numerous searches for simplistic ways to do it. One result of this concentration of effort was the tomahawk. (Mathematicians, it seems, often beat to death problems that have only limited practical application.)

All this noodling went on in the days before our high accuracy goniometers, digital computers, and other precision approaches to solving the problem. Still the simplicity of the tomahawk is a tribute to the ingenuity of the human mind.