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It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

Lockwood (1957) terms the ellipse negative pedal curve with pedal point at the focus "Burleigh's oval" in honor of his student M. J. Burleigh, who first drew his attention to ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

A link L is said to be splittable if a plane can be embedded in R^3 such that the plane separates one or more components of L from other components of L and the plane is ...

In the above figure, let E be the intersection of AD and BC and specify that AB∥EF∥CD. Then 1/(AB)+1/(CD)=1/(EF). A beautiful related theorem due to H. Stengel can be stated ...

An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

The Euler triangle of a triangle DeltaABC is the triangle DeltaE_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective ...

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

The space join of a topological space X and a point P, C(X)=X*P.