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The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

A cylindrical segment, sometimes also called a truncated cylinder, is the solid cut from a circular cylinder by two (or more) planes. If there are two cutting planes, one ...

How many times can a shape be completely surrounded by copies of itself without being able to tile the entire plane, i.e., what is the maximum (finite) Heesch number?

Increasing a plane figure's linear dimensions by a scale factor s increases the perimeter p^'->sp and the area A^'->s^2A.

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

Let a, b, and c be the side lengths of a reference triangle DeltaABC. Now let A_b be a point on the extension of the segment CA beyond A such that AA_b=a. Similarly, define ...

The locus of a point P (or the envelope of a line) fixed in relation to a curve C which slides between fixed curves. For example, if C is a line segment and P a point on the ...

The M'Cay cubic Z(X_3) is a self-isogonal cubic given by the locus of all points whose pedal circle touches the nine-point circle, or equivalently, the locus of all points P ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

Given a point with trilinear coordinates P=alpha:beta:gamma, the anticevian triangle DeltaA^'B^'C^' of a triangle DeltaABC with respect to P is a triangle such that 1. B^'C^' ...