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Tomahawk


Tomahawk

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and is equal to the radius, and a segment SV perpendicular to it.

It can be used to trisect an angle, an operation impossible with straightedge and compass. If it is adjusted to an the angle ABC so that

1. The line AB passes through R.

2. B lies on line SV.

3. The line BC is tangent to the semicircle.

Then angle ∠SBT is equal to one third of ∠ABC.

The interesting fact about the tomahawk is that it can be easily constructed with straightedge and compass. Hence these tools are, from a merely practical point of view, sufficient to trisect an angle. This does not contradict what is known from mathematical theory, since the procedure of shifting a figure on the paper until its parts fall in given positions is not an Euclidean construction.


See also

Angle Trisection

This entry contributed by Margherita Barile

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References

Eves, H. An Introduction to the History of Mathematics, 3rd ed. New York: Holt, Rinehart and Winston, pp. 86-87, 1969.Loomis, E. S. "The Tomahawk." §3.7 in The Pythagorean Proposition: Its Demonstrations Analyzed and Classified and Bibliography of Sources for Data of the Four Kinds of "Proofs," 2nd ed. Reston, VA: National Council of Teachers of Mathematics, p. 37, 1968.Loy, J. "Trisection of an Angle." http://www.jimloy.com/geometry/trisect.htm.

Referenced on Wolfram|Alpha

Tomahawk

Cite this as:

Barile, Margherita. "Tomahawk." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Tomahawk.html

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