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For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.

A representation of a C^*-algebra A is a pair (H,phi) where H is a Hilbert space and phi:A->B(H) is a *-homomorphism. (H,phi) is said to be faithful if phi is injective. For ...

A Cevian point P is point with respect to which a set of Cevians of a triangle are taken. Connecting the endpoints of the Cevians through a point P gives the so-called Cevian ...

The end values which specify a class interval.

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

Values one step outside the hinges are called inner fences, and values two steps outside the hinges are called outer fences. Tukey calls values outside the outer fences far ...

The first Neuberg circle is the circumcircle of the first Neuberg triangle. The center has center function (1) which is not a Kimberling center. Its radius is ...

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...