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The symbol ∡ABC denotes the directed angle from AB to BC, which is the signed angle through which AB must be rotated about B to coincide with BC. Four points ABCD lie on a ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

∡A_2MA_3=∡A_2A_1A_3+∡P_2P_1P_3, where ∡ is a directed angle.

In the triangle DeltaABC illustrated above, side c subtends angle ∠C. More generally, given a geometric object O in the plane and a point P, let A be the angle from one edge ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

A magic square for which the number of letters in the word for each number generates another magic square. This definition depends, of course, on the language being used. In ...

The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be ...

A causal network is an acyclic digraph arising from an evolution of a substitution system, and representing its history. The illustration above shows a causal network ...

An (infinite) line determined by two points (x_1,y_1) and (x_2,y_2) may intersect a circle of radius r and center (0, 0) in two imaginary points (left figure), a degenerate ...

Ellipses sharing common foci (left figure). The family of confocal ellipses covers the plane simply, in the sense that there is a unique ellipse passing through each point in ...