Transcendental Curves

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Here is the involute of a circle, along with its parametric equation.
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Here is an Epi Spiral, shown with its polar equation
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Here are Poinsot's two spirals. The one in red is given by the equation r*cosh(n*T), while the one in blue is r*sinh(n*T)
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This curve has an asymptote at the origin and was originally studied by Bernoulli in 1726.
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The cycloid is defined as the locus of a point on the circumference of a circle rolling along a line.
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The caternary, also known as the chainette and the alysoid, describes the form assumed by a perfect flexible chain of uniform density hanging from two...
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Archimedes' spiral is the Archimedean spiral with the polar equation shown below.
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An Archimedean spiral is a spiral with a constant "m" that determines how tightly the spiral is wrapped.
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Fermat's spiral is the Archimedean spiral with m=2. Both the left-hand and right-hand spirals are shown below.
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The Hyperbolic spiral is the Archimedean spiral with m=(-1).
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The Lituus is the Archimedean spiral with m=(-2). Both the left-hand and right-hand spirals are shown below.
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The Logarithmic spiral is the locus of the equations shown below.
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The Sinusoidal spiral is the locus of the equations shown below.
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The Tractrix is the evolute of the catnary.
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A Curtate cycloid is a cycloid where the locus is drawn from a point closer to the center of the circle than the circle's circumference.
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A Prolate cycloid is a cycloid where the locus is drawn from a point farther from the center of the circle than the circle's circumference.
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