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Tomahawk (geometry)
The tomahawk is a tool in geometry for angle trisection, the problem of splitting an angle into three equal parts. The boundaries of its shape include a semicircle and two line segments, arranged in a way that resembles a tomahawk, a Native American axe.〔〔 The same tool has also been called the shoemaker's knife,〔.〕 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).〔.〕
==Description==
The basic shape of a tomahawk consists of a semicircle (the "blade" of the tomahawk), with a line segment the length of the radius extending along the same line as the diameter of the semicircle (the tip of which is the "spike" of the tomahawk), and with another line segment of arbitrary length (the "handle" of the tomahawk) perpendicular to the diameter. In order to make it into a physical tool, its handle and spike may be thickened, as long as the line segment along the handle continues to be part of the boundary of the shape. 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.〔.〕
In some sources a full circle rather than a semicircle is used,〔 or the tomahawk is also thickened along the diameter of its semicircle,〔 but these modifications make no difference to the action of the tomahawk as a trisector.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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