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In 1989, P. Yff proved there is a unique configuration of isoscelizers for a given triangle such that all three have the same length and are concurrent (C. Kimberling, pers. ...

The coversine is a little-used entire trigonometric function defined by covers(z) = versin(1/2pi-z) (1) = 1-sinz, (2) where versin(z) is the versine and sinz is the sine. The ...

A curve whose name means skull-like. It is given by the polar equation r=asint+bsqrt(1-pcos^2t)+csqrt(1-qcos^2t), where a,b,c>0, a<b+c, 0<p<1, 0<q<1, and p!=q. The top of the ...

Let F be the Maclaurin series of a meromorphic function f with a finite or infinite number of poles at points z_k, indexed so that 0<|z_1|<=|z_2|<=|z_3|<=..., then a pole ...

A dependent variable is a variable whose value depends on the values of one or more other independent variables. This notion comes up regularly in a variety of contexts. In ...

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0) in the direction u. It is a vector form of the ...

A.k.a. the pigeonhole principle. Given n boxes and m>n objects, at least one box must contain more than one object. This statement has important applications in number theory ...

If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

The first Napoleon point N, also called the outer Napoleon point, is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of ...