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For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

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.

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

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 ...

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 ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

A number x in which the first n decimal digits of the fractional part frac(x) sum to 666 is known as an evil number (Pegg and Lomont 2004). However, the term "evil" is also ...

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...