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A system for specifying points using coordinates measured in some specified way. The simplest coordinate system consists of coordinate axes oriented perpendicularly to each ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The pedal curve of an epicycloid x = (a+b)cost-b[((a+b)t)/b] (1) y = (a+b)sint-bsin[((a+b)t)/b] (2) with pedal point at the origin is x_p = 1/2(a+2b){cost-cos[((a+b)t)/b]} ...

Given collinear points W, X, Y, and Z, Y and Z are harmonic conjugates with respect to W and X if (|WY|)/(|YX|)=(|WZ|)/(|XZ|). (1) W and X are also harmonic conjugates with ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

A real-valued univariate function f=f(x) is said to have an infinite discontinuity at a point x_0 in its domain provided that either (or both) of the lower or upper limits of ...

The sphere with respect to which inverse points are computed (i.e., with respect to which geometrical inversion is performed). For example, the cyclides are inversions in a ...

The geometry resulting from the application of the inversion operation. It can be especially powerful for solving apparently difficult problems such as Steiner's porism and ...

If mu is a real measure (i.e., a measure that takes on real values), then one can decompose it according to where it is positive and negative. The positive variation is ...

A real-valued univariate function f=f(x) has a jump discontinuity at a point x_0 in its domain provided that lim_(x->x_0-)f(x)=L_1<infty (1) and lim_(x->x_0+)f(x)=L_2<infty ...