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The sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate.

A number n is called a k e-perfect number if sigma_e(n)=kn, where sigma_e(n) is the sum of the e-divisors of n.

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

A special case of Hölder's sum inequality with p=q=2, (sum_(k=1)^na_kb_k)^2<=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2), (1) where equality holds for a_k=cb_k. The inequality is ...

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

A Meeussen sequence is an increasing sequence of positive integers (m_1, m_2, ...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each ...

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

sum_(n=1)^(infty)1/(phi(n)sigma_1(n)) = product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1))) (1) = 1.786576459... (2) (OEIS A093827), where phi(n) is the totient function ...

A projective module generalizes the concept of the free module. A module M over a nonzero unit ring R is projective iff it is a direct summand of a free module, i.e., of some ...