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The Sombor matrix A_(Sombor) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the graph. In ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

The order ideal in Lambda, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot K. Any generator of a principal Alexander ideal is called ...

A number of the form p^a·A is said to be an antisquare if it fails to be a square number for the two reasons that a is odd and A is a nonsquare (modulo p). The first few ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...

The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x. For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for ...