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Pogson's ratio is the constant 100^(1/5)=10^(2/5)=2.511886431... (OEIS A189824) appearing in the definition of the astronomical magnitude (brightness) scale. This scale is ...

An analytic refinement of results from complex analysis such as those codified by Picard's little theorem, Picard's great theorem, and the Weierstrass-Casorati theorem.

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Let m>=3 be an integer and let f(x)=sum_(k=0)^na_kx^(n-k) be an integer polynomial that has at least one real root. Then f(x) has infinitely many prime divisors that are not ...

The finite zeros of the derivative r^'(z) of a nonconstant rational function r(z) that are not multiple zeros of r(z) are the positions of equilibrium in the field of force ...

If f(z) is regular and of the form O(e^(k|z|)) where k<pi, for R[z]>=0, and if f(z)=0 for z=0, 1, ..., then f(z) is identically zero.

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.

If f:[a,b]->[a,b] (where [a,b] denotes the closed interval from a to b on the real line) satisfies a Lipschitz condition with constant K, i.e., if |f(x)-f(y)|<=K|x-y| for all ...

The lines joining the vertices A, B, and C of a given triangle DeltaABC with the circumcenters of the triangles DeltaBCO, DeltaCAO, and DeltaABO (where O is the circumcenter ...