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A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...

The Maltese cross is a symbol identified with the Christian warrior whose outward points form an octagon (left figure). Another class of cross sometimes (incorrectly) known ...

A general formula giving the number of distinct ways of folding an m×n rectangular map is not known. A distinct folding is defined as a permutation of N=m×n numbered cells ...

The Mephisto waltz sequence is defined by beginning with 0 and then iterating the maps 0->001 and 1->110. This gives 0, 001, 001001110, 001001110001001110110110001, ... (OEIS ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

A numeral is a symbol used to represent a number. Arabic numerals (0-9) are the ones most commonly used today. Other types, mainly of historical interest, include Egyptian, ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...