Wittgenstein's rod
Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.
Description
A ray is drawn with its origin on a circle, through an external point and a point is chosen at some constant distance from the starting end of the ray; what figure does describe when all the initial points on the circle are considered? The answer depends on three parameters: the radius of the circle, the distance from the center to, and the length of the segment. The shape described by can be seen as a 'figure-eight' which in some cases degenerates to a single lobe looking like an inverted cardioid.If remains on the same side of with respect to the center of the circle, instead of a ray one can consider just a segment or the rod.
Wittgenstein sketched a mechanism and wrote:
This text has been included among the notes selected for publication in Remarks on the Foundations of Mathematics and the editors have dated in the as spring of 1944.