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The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

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 ...

The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. The spheres can be used to show that the ...

The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

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 ...

The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...