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It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

Let u_(p) be a unit tangent vector of a regular surface M subset R^3. Then the normal curvature of M in the direction u_(p) is kappa(u_(p))=S(u_(p))·u_(p), (1) where S is the ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

A weakly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in some direction (i.e., not ...

Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A ...

A triangle center function (sometimes simply called a center function) is a nonzero function f(a,b,c) that is homogeneous f(ta,tb,tc)=t^nf(a,b,c) (1) bisymmetry in b and c, ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...