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The integral of 1/r over the unit disk U is given by intint_(U)(dA)/r = intint_(U)(dxdy)/(sqrt(x^2+y^2)) (1) = int_0^(2pi)int_0^1(rdrdtheta)/r (2) = 2piint_0^1dr (3) = 2pi. ...

A ball of radius 1.

The Eisenstein units are the Eisenstein integers +/-1, +/-omega, +/-omega^2, where omega = 1/2(-1+isqrt(3)) (1) omega^2 = 1/2(-1-isqrt(3)). (2)

A parallelogram (parallelepiped) containing the minimum repeatable elements of a circle (sphere) packing.

A sphere of radius 1.

1 and -1 are the only integers which divide every integer. They are therefore called the prime units.

The point in the plane with Cartesian coordinates (1, 1).

Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r=r_1+r_2-1. Then the multiplicative group of units U_K of K has the form ...

A distance graph with distance set (0,1].

An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).