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For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

The jinc function is defined as jinc(x)=(J_1(x))/x, (1) where J_1(x) is a Bessel function of the first kind, and satisfies lim_(x->0)jinc(x)=1/2. The derivative of the jinc ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

When a number is expressed in scientific notation, the number of significant digits (or significant figures) is the number of digits needed to express the number to within ...

The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

A number of the form a_0+a_1zeta+...+a_(p-1)zeta^(p-1), where zeta=e^(2pii/p) is a de Moivre number and p is a prime number. Unique factorizations of cyclotomic integers fail ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...

The normal vector, often simply called the "normal," to a surface is a vector which is perpendicular to the surface at a given point. When normals are considered on closed ...