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Wittgenstein's rod is a problem in
Geometer's Sketchpad applet
{{DEFAULTSORT:Wittgenstein's Rod Geometry Rod Linkages (mechanical)
Wittgenstein's rod is a problem in geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
discussed by 20th-century philosopher Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is con ...
.
Description
A ray is drawn with its origin on acircle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is con ...
, 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
In geometry, a cardioid () is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal ...
.
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.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
Related mechanism
Wittgenstein's rod is a generalization of Hoeckens linkage.Animations
See also
*Oscillating cylinder steam engine
An oscillating cylinder steam engine (also known as a wobbler in the US) is a simple steam-engine design (proposed by William Murdoch at the end of 18th century) that requires no valve gear. Instead the cylinder rocks, or oscillates, as the ...
— a steam engine using a Wittgenstein's rod scribing a figure-of-eight shape (it does not make use of the curve scribed)
References
External links
Geometer's Sketchpad applet
{{DEFAULTSORT:Wittgenstein's Rod Geometry Rod Linkages (mechanical)