In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, Poinsot's spirals are two
spiral
In mathematics, a spiral is a curve which emanates from a point, moving further away as it revolves around the point. It is a subtype of whorled patterns, a broad group that also includes concentric objects.
Two-dimensional
A two-dimension ...
s represented by the
polar equation
In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are
*the point's distance from a reference point called the ''pole'', and
*the point's direction from ...
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 un ...
, 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 unit circle, circle with a unit radius, the points form the right ha ...
.
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 ...
.
Examples of the two types of Poinsot's spirals
See also
*
References
Spirals
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