Search Results for ""

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

The number two (2) is the second positive integer and the first prime number. It is even, and is the only even prime (the primes other than 2 are called the odd primes). The ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

A number k such that nk^2 has its last digit(s) equal to k is called n-automorphic. For example, 1·5__^2=25__ (Wells 1986, pp. 58-59) and 1·6__^2=36__ (Wells 1986, p. 68), so ...

A class of complete orientable minimal surfaces of R^3 derived from Enneper's minimal surface. They are named for the mathematicians who found the first two examples in 1982. ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...