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Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

A recursive primality certificate for a prime p. The certificate consists of a list of 1. A point on an elliptic curve C y^2=x^3+g_2x+g_3 (mod p) for some numbers g_2 and ...

An equation representing a locus L in the n-dimensional Euclidean space. It has the form L:f(x_1,...,x_n)=0, (1) where the left-hand side is some expression of the Cartesian ...

The cochleoid, whose name means "snail-form" in Latin, was first considered by John Perks as referenced in Wallis et al. (1699). The cochleoid has also been called the oui-ja ...

Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

A plane curve proposed by Descartes to challenge Fermat's extremum-finding techniques. In parametric form, x = (3at)/(1+t^3) (1) y = (3at^2)/(1+t^3). (2) The curve has a ...

Lagrange multipliers, also called Lagrangian multipliers (e.g., Arfken 1985, p. 945), can be used to find the extrema of a multivariate function f(x_1,x_2,...,x_n) subject to ...

A right strophoid is the strophoid of a line L with pole O not on L and fixed point O^' being the point where the perpendicular from O to L cuts L is called a right ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...