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The first mid-arc point is the triangle center with triangle center function alpha_(178)=[cos(1/2B)+cos(1/2C)]csc(1/2A). It is Kimberling center X_(178).

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

Let (L,<=) be any complete lattice. Suppose f:L->L is monotone increasing (or isotone), i.e., for all x,y in L, x<=y implies f(x)<=f(y). Then the set of all fixed points of f ...

Given a decimal-valued floating-point operation in the IEEE 754-2008 standard, the preferred exponent is the value of the exponent q which preserves the quantum of the ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

Picking two independent sets of points x and y from a unit uniform distribution and placing them at coordinates (x,y) gives points uniformly distributed over the unit square. ...

It is conjectured that any convex body in n-dimensional Euclidean space has an interior point lying on normals through 2n distinct boundary points (Croft et al. 1991). This ...

A point process N on R is said to be interval stationary if for every r=1,2,3,... and for all integers i_i,...,i_r, the joint distribution of {tau_(i_1+k),...,tau_(i_r+k)} ...

A formula for numerical solution of differential equations, (1) where k_1 = hf(x_n,y_n) (2) k_2 = hf(x_n+1/2h,y_n+1/2k_1) (3) k_3 = ...