The tomahawk is a "tool" in geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 consisting of a semicircle and two line segments. The basic shape

Shape

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...

 is constructible with compass and straightedge

Compass and straightedge

Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass....

. It is possible to trisect an angle with the tomahawk. This does not contradict the usual theorem stating that an arbitrary angle cannot be trisected

Angle trisection

Angle trisection is a classic problem of compass and straightedge constructions of ancient Greek mathematics. It concerns construction of an angle equal to one-third of a given arbitrary angle, using only two tools: an un-marked straightedge, and a compass....

 by compass and unmarked straightedge alone, as translating the constructed tomahawk into the required position is not a Euclidean construction

Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

.

External links

• MathWorld/Wolfram contains other references
• Jim Loy "cheating using other tools"
• Angle Trisection Problem: Trisect An Angle With a Tomahawk at ArticlesForEducators.com