Wittgenstein's rod explained

Wittgenstein's rod should not be confused with Wittgenstein's Poker.

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.[1]

Related mechanism

Wittgenstein's rod is a generalization of Hoeckens linkage.

Animations

See also

References

  1. Wittgenstein L., Remarks on the Foundations of Mathematics, edited by G. H. von Wright and Rush Rhees, Oxford: Blackwell 1998,, sect V, §72, p.434

External links