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A minor M_(ij) is the reduced determinant of a determinant expansion that is formed by omitting the ith row and jth column of a matrix A. So, for example, the minor M_(22) of ...

Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...

Consider a convex pentagon and extend the sides to a pentagram. Externally to the pentagon, there are five triangles. Construct the five circumcircles. Each pair of adjacent ...

Three guests decide to stay the night at a lodge whose rate they are initially told is $30 per night. However, after the guests have each paid $10 and gone to their room, the ...

Polynomials M_k(x) which form the associated Sheffer sequence for f(t)=(e^t-1)/(e^t+1) (1) and have the generating function sum_(k=0)^infty(M_k(x))/(k!)t^k=((1+t)/(1-t))^x. ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...

The mode of a set of observations is the most commonly occurring value. For example, for a data set (3, 7, 3, 9, 9, 3, 5, 1, 8, 5) (left histogram), the unique mode is 3. ...

Model theory is a general theory of interpretations of axiomatic set theory. It is the branch of logic studying mathematical structures by considering first-order sentences ...

The second-order ordinary differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)-(x^2+n^2)y=0. (1) The solutions are the modified Bessel functions of the first and second kinds, ...