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At the points where a line X cuts the sides of a triangle DeltaA_1A_2A_3, draw three perpendiculars to the sides, one through each point of intersection. The resulting three ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...

The golden ratio phi can be written in terms of a nested radical in the beautiful form phi=sqrt(1+sqrt(1+sqrt(1+sqrt(1+...)))), (1) which can be written recursively as ...

Given a linear code C of length n and dimension k over the field F, a parity check matrix H of C is a n×(n-k) matrix whose rows generate the orthogonal complement of C, i.e., ...

The Parry point is one of the two intersections of the Parry circle and the circumcircle of a triangle (the other is the focus of the Kiepert parabola, which is Kimberling ...

Let L, M, and N be lines through A, B, C, respectively, parallel to the Euler line. Let L^' be the reflection of L in sideline BC, let M^' be the reflection of M in sideline ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...

A permutation of n distinct, ordered items in which none of the items is in its original ordered position is known as a derangement. If some, but not necessarily all, of the ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...