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The position of a rational number in the sequence 1/1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ..., ordered in terms of increasing numerator+denominator.

In the American system, 10^(51).

In the American system, 10^(21).

An algorithm which finds the least nonnegative value of sqrt(a (mod p)) for given a and prime p.

A translation without rotation or distortion.

The edge of a polygon or face of a polyhedron are sometimes called sides.

To multiply the size of a d-D object by a factor a, c=a^d copies are required, and the quantity d=(lnc)/(lna) is called the similarity dimension.

The type of homology which results when the spaces being studied are restricted to simplicial complexes and subcomplexes.

If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).

The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...