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Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

The common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

A regular number, also called a finite decimal (Havil 2003, p. 25), is a positive number that has a finite decimal expansion. A number such as 1/3=0.33333... which is not ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

Let T be a tree defined on a metric over a set of paths such that the distance between paths p and q is 1/n, where n is the number of nodes shared by p and q. Let A be a ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...

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 ...

The Dottie number is the name given by Kaplan (2007) to the unique real root of cosx=x (namely, the unique real fixed point of the cosine function), which is 0.739085... ...

The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...