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The mid-arc triangle is the triangle DeltaA^'B^'C^' whose vertices consist of the intersections of the internal angle bisectors with the incircle, where the points of ...

The midcircle of two given circles is the circle which would invert the circles into each other. Dixon (1991) gives constructions for the midcircle for four of the five ...

A plot of the cells on a grid satisfying bitwise XOR(a,b)<n for consecutive values of n=1, 2, .... It is thought that it was discovered by Jackson Wright on the RLE PDP-1 ...

A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice" (i.e., branch) of the function chosen that is for ...

A real-valued function g defined on a convex subset C subset R^n is said to be quasi-concave if for all real alpha in R, the set {x in C:g(x)>=alpha} is convex. This is ...

A real-valued function g defined on a convex subset C subset R^n is said to be quasi-convex if for all real alpha in R, the set {x in C:g(x)<alpha} is convex. This is ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...