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A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral ...

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

A three-dimensional coordinate system in which the axes do not satisfy the right-hand rule.

Let suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

Two curves phi and psi satisfying phi+psi=0 are said to be linearly dependent. Similarly, n curves phi_i, i=1, ..., n are said to be linearly dependent if sum_(i=1)^nphi_i=0.

Loess local regression is a nonparametric technique for describing bivariate relationships where the functional form is not known in advance.

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

A compact manifold admits a Lorentzian structure iff its Euler characteristic vanishes. Therefore, every noncompact manifold admits a Lorentzian structure.