Wittgenstein's rod
Encyclopedia
Wittgenstein's rod is a geometry problem attributed to 20th century philosopher Ludwig Wittgenstein
.
The set-up is as follows: a rod
passes through a sleeve, in which it can smoothly slide. The sleeve is tangentially affixed to a wall at its lengthwise center, forming a pivot. One end of the rod is moved in a circle whose plane is parallel to the wall. The question of the thought experiment is what shape does the other end of the rod describe?
The seemingly obvious answer is a circle
, but in fact it describes an invert
ed cardioid
.
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
.
The set-up is as follows: a rod
Rod (geometry)
In geometry, a rod is a three-dimensional, solid cylinder....
passes through a sleeve, in which it can smoothly slide. The sleeve is tangentially affixed to a wall at its lengthwise center, forming a pivot. One end of the rod is moved in a circle whose plane is parallel to the wall. The question of the thought experiment is what shape does the other end of the rod describe?
The seemingly obvious answer is a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
, but in fact it describes an invert
Inverse curve
In geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle with center O and radius k the inverse of a point Q is the point P for which P lies on the ray OQ and OP·PQ = k2...
ed cardioid
Cardioid
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 is therefore a type of limaçon and can also be defined as an epicycloid having a single cusp...
.