In
mathematics, Poinsot's spirals are two
spirals represented by the
polar equation
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to th ...
s
:
:
where csch is the
hyperbolic cosecant
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the u ...
, and sech is the
hyperbolic secant
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the un ...
.
They are named after the French mathematician
Louis Poinsot
Louis Poinsot (3 January 1777 – 5 December 1859) was a French mathematician and physicist. Poinsot was the inventor of geometrical mechanics, showing how a system of forces acting on a rigid body could be resolved into a single force and a c ...
.
Examples of the two types of Poinsot's spirals
See also
*
Cotes's spiral
References
Spirals
{{geometry-stub