Wittgenstein's rod
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Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.
Description
A ray is drawn with its origin Template:Mvar on a circle, through an external point Template:Mvar and a point Template:Mvar is chosen at some constant distance from the starting end of the ray; what figure does Template:Mvar 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 Template:Mvar, and the length of the segment Template:Mvar. The shape described by Template:Mvar can be seen as a 'figure-eight' which in some cases degenerates to a single lobe looking like an inverted cardioid.
If Template:Mvar remains on the same side of Template:Mvar with respect to the center of the circle, instead of a ray one can consider just a segment or the rod Template:Mvar.
Wittgenstein sketched a mechanism and wrote:
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While the point A describes a circle, B describes a figure eight. Now we write this down as a proposition of kinematics.
When I work the mechanism its movement proves the proposition to me; as would a construction on paper. The proposition corresponds e.g. to a picture of the mechanism with the paths of the points A and B drawn in. Thus it is in a certain respect a picture of that movement. It holds fast what the proof shows me. Or – what it persuades me of.{{#if:|
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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.<ref>Wittgenstein L., Remarks on the Foundations of Mathematics, edited by G. H. von Wright and Rush Rhees, Oxford: Blackwell 1998, Template:ISBN, sect V, §72, p.434</ref>
Related mechanism
Wittgenstein's rod is a generalization of Hoeckens linkage.
Animations
See also
- Oscillating cylinder steam engine — a steam engine using a Wittgenstein's rod scribing a figure-of-eight shape (it does not make use of the curve scribed)
References
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