Spirals

Hyperbolic spiral

A hyperbolic spiral is a plane curve, which can be described in polar coordinates by the equation of a hyperbola. Because it can be generated by a circle inversion of an Archimedean spiral, it is called Reciprocal spiral, too. Pierre Varignon first studied the curve in 1704. Later Johann Bernoulli and Roger Cotes worked on the curve as well. The hyperbolic spiral has a pitch angle that increases with distance from its center, unlike the logarithmic spiral (in which the angle is constant) or Archimedean spiral (in which it decreases with distance). For this reason, it has been used to model the shapes of spiral galaxies, which in some cases similarly have an increasing pitch angle. However, this model does not provide a good fit to the shapes of all spiral galaxies. (Wikipedia).

Hyperbolic spiral
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From playlist Summer of Math Exposition 2 videos

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From playlist The Hyperbola in Conic Sections

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From playlist The Hyperbola in Conic Sections

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From playlist Universal Hyperbolic Geometry

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From playlist Graphing and Writing Equations of Hyperbolas

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From playlist MathSeminars

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From playlist Mathematics 1A (Calculus)

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From playlist Celebration of Mind 2021

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From playlist Public Lectures

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Related pages

Hyperbola | Johann Bernoulli | Pierre Varignon | Spiral galaxy | Polar coordinate system | Archimedean spiral | Roger Cotes | Osculating circle | Plane curve