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A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

The pedal curve of an ellipse with parametric equations x = acost (1) y = bsint (2) and pedal point (x_0,y_0) is given by f = ...

There are two theorems commonly known as Feuerbach's theorem. The first states that circle which passes through the feet of the perpendiculars dropped from the polygon ...

Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

The locus of a point which is derived from a fixed point Q by continuous parallel displacement.

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

The Fermat axis is the central line connecting the first and second Fermat points. It has line function l=a(b^2-c^2)(a^2-b^2-bc-c^2)(a^2-b^2+bc-c^2), corresponding to ...

The inconic having inconic parameters x:y:z=a/(b+c-a):b/(a+c-b):c/(a+b-c). Its center is the mittenpunkt M of the triangle and its Brianchon point is the Nagel point Na. The ...

Two triangles DeltaABC and DeltaA^'B^'C^' are said to be perspective, or sometimes homologic, from a line if the extensions of their three pairs of corresponding sides meet ...

The covering of a plane curve with disks of radius epsilon whose centers lie on the curve.