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A hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle. The curves above correspond to values of a=0.1, 0.2, ..., 1.0. Additional attractive ...

Let L be a language of the first-order logic. Assume that the language L has the following sets of nonlogical symbols: 1. C is the set of constant symbols of L. (These are ...

Let U subset= C be an open set and f a real-valued continuous function on U. Suppose that for each closed disk D^_(P,r) subset= U and every real-valued harmonic function h ...

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 ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

A kit consisting of colored rods and slotted balls that can be used to construct three-dimensional configurations. The balls into which the rods are placed resemble an ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...