Figure 1: compass

A mathematical machine (in geometry) is an artefact that has no practical purpose and is designed to force a point, a line segment or a plane figure (supported in a way as to make it visible and touchable) to move according to a mathematical law determined by the designer. The most well-known mathematical machine is the pair of compasses (to draw circles) that is part of the iconography of mathematicians (Fig. 1). It is the ancestor of many curve drawing devices and pantographs. Another class of mathematical machines is given by perspectographs (e.g. Fig. 2), which are related to the ancient three-dimensional theory of conics, on one hand, and the roots of projective geometry on the other