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Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

Let (A,<=) be a well ordered set. Then the set {a in A:a<k} for some k in A is called an initial segment of A (Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore 1982, pp. ...

The initial side of an angle theta drawn in angle standard position is the side lying on the positive x-axis. In general, viewing an angle as the amount of rotation about the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the incircle (with center I) and the A-excircle (with center J_A). Of these, three correspond to the ...

An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

A system of coordinates obtained by inversion of the oblate spheroids and one-sheeted hyperboloids in oblate spheroidal coordinates. The inverse oblate spheroidal coordinates ...

A semigroup S is said to be an inverse semigroup if, for every a in S, there is a unique b (called the inverse of a) such that a=aba and b=bab. This is equivalent to the ...

An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where ...

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...