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A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

Scientific notation is the expression of a number n in the form a×10^p, where p=|_log_(10)|n|_| (1) is the floor of the base-10 logarithm of n (the "order of magnitude"), and ...

Given a Seifert form f(x,y), choose a basis e_1, ..., e_(2g) for H_1(M^^) as a Z-module so every element is uniquely expressible as n_1e_1+...+n_(2g)e_(2g) (1) with n_i ...

Let x be a positive number, and define lambda(d) = mu(d)[ln(x/d)]^2 (1) f(n) = sum_(d)lambda(d), (2) where the sum extends over the divisors d of n, and mu(n) is the Möbius ...

A semimagic square is a square that fails to be a magic square only because one or both of the main diagonal sums do not equal the magic constant (Kraitchik 1942, p. 143). ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

A siteswap is a sequence encountered in juggling in which each term is a positive integer, encoded in binary. The transition rule from one term to the next consists of ...