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Draw three circles in the plane, none of which lies completely inside another, and the common external tangent lines for each pair. Then points of intersection of the three ...

The base 8 notational system for representing real numbers. The digits used are 0, 1, 2, 3, 4, 5, 6, and 7, so that 8_(10) (8 in base 10) is represented as 10_8 ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

Let X be a set of urelements, and let V(X) be the superstructure with X as its set of individuals. Let kappa be a cardinal number. An enlargement V(^*X) is kappa-saturated ...

Schur's partition theorem lets A(n) denote the number of partitions of n into parts congruent to +/-1 (mod 6), B(n) denote the number of partitions of n into distinct parts ...

In the above illustration, black dots appear to form and vanish at the intersections of the gray horizontal and vertical lines. When focusing attention on a single white dot, ...

The Seidel-Entringer-Arnold triangle is the number triangle consisting of the Entringer numbers E_(n,k) arranged in "ox-plowing" order, ...

A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between ...

Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the ...