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The definite integral int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1, (1) where a, b, and x are real numbers and lnx is the natural logarithm.

Chained arrow notation is a notation which generalizes the Knuth up-arrow notation and is defined as a^...^b_()_(c)=a->b->c.

A surface with tetrahedral symmetry which looks like an inflatable chair from the 1970s. It is given by the implicit equation The surface illustrated above has k=5, a=0.95, ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted ...

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->..., the module B^i of i-coboundaries is the image of d^(i-1). It is a submodule of C^i and is ...

Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with ...

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...