Search Results for ""

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

If a complex function is analytic at all finite points of the complex plane C, then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112). Any ...

Eternity is a puzzle devised by Christopher Monckton and consisting of 209 pieces, each of which is a 12-polydrafter (i.e., a compound of 30-60-90 triangles). The puzzle was ...

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

The Euler triangle of a triangle DeltaABC is the triangle DeltaE_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective ...

Euler conjectured that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... In fact, MacNeish (1921-1922) published a purported proof of this conjecture (Bruck ...

The W polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. (The corresponding w polynomials are called Lucas polynomials.) They have explicit ...

A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...