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Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

A square pyramid is a pyramid with a square base. It is a pentahedron. The lateral edge length e and slant height s of a right square pyramid of side length a and height h ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

An isolated singularity is a singularity for which there exists a (small) real number epsilon such that there are no other singularities within a neighborhood of radius ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

Zeros of the Riemann zeta function zeta(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s=-2, -4, -6, ..., and "nontrivial ...