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The pedal curve of circle involute f = cost+tsint (1) g = sint-tcost (2) with the center as the pedal point is the Archimedes' spiral x = tsint (3) y = -tcost. (4)

Let a, b, and c be the side lengths of a reference triangle DeltaABC. Now let A_b be a point on the extension of the segment CA beyond A such that AA_b=a. Similarly, define ...

The Janko groups are the four sporadic groups J_1, J_2, J_3 and J_4. The Janko group J_2 is also known as the Hall-Janko group. The Janko groups are implemented in the ...

An integer sequence whose terms are defined in terms of number-related words in some language. For example, the following table gives the sequences of numbers having digits ...

Each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition.

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

The radial curve of a unit circle from a radial point (x,y) and parametric equations x = cost (1) y = sint (2) is another circle with parametric equations x_r = x-cost (3) ...

An n-dimensional open ball of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Explicitly, the open ball with center x ...