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There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

An extended form of Bürmann's theorem. Let f(z) be a function of z analytic in a ring-shaped region A, bounded by another curve C and an inner curve c. Let theta(z) be a ...

Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

A triangle cubic is a curve that can be expressed in trilinear coordinates such that the highest degree term in the trilinears alpha, beta, and gamma is of order three. Wells ...

A curve which can be used to trisect an angle. Although an arbitrary angle cannot be trisected using only compass and straightedge (i.e., according to the strict rules of ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

Calculus II

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...