Tomahawk (geometry)

The boundaries of its shape include a semicircle and two line segments, arranged in a way that resembles a tomahawk, a Native American axe.

[1][2] The same tool has also been called the shoemaker's knife,[3] but that name is more commonly used in geometry to refer to a different shape, the arbelos (a curvilinear triangle bounded by three mutually tangent semicircles).

Unlike a related trisection using a carpenter's square, the other side of the thickened handle does not need to be made parallel to this line segment.

One of the two trisecting lines then lies on the handle segment, and the other passes through the center point of the semicircle.

It dates back at least as far as 1835, when it appeared in a book by Claude Lucien Bergery, Géométrie appliquée à l'industrie, à l'usage des artistes et des ouvriers (3rd edition).

A tomahawk, with its handle and spike thickened
A tomahawk trisecting an angle . The handle AD forms one trisector and the dotted line AC to the center of the semicircle forms the other.