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A triangle center is regular iff there is a triangle center function which is a polynomial in Delta, a, b, and c (where Delta is the area of the triangle) such that the ...

The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such ...

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

Let theta be the angle between two vectors. If 0<theta<pi, the vectors are positively oriented. If pi<theta<2pi, the vectors are negatively oriented. Two vectors in the plane ...

Given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles. One can easily prove that vertical angles are congruent. Some ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...

If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...