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A link L is said to be splittable if a plane can be embedded in R^3 such that the plane separates one or more components of L from other components of L and the plane is ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...

Lockwood (1957) terms the ellipse negative pedal curve with pedal point at the focus "Burleigh's oval" in honor of his student M. J. Burleigh, who first drew his attention to ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

Chebyshev noticed that the remainder upon dividing the primes by 4 gives 3 more often than 1, as plotted above in the left figure. Similarly, dividing the primes by 3 gives 2 ...

The function defined by U(p)=(p#)^(p#), where p is a prime number and p# is a primorial. The values for p=2, 3, ..., are 4, 46656, ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...

The matrix operations of 1. Interchanging two rows or columns, 2. Adding a multiple of one row or column to another, 3. Multiplying any row or column by a nonzero element.

The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...