Search Results for ""

Hoggatt and Denman (1961) showed that any obtuse triangle can be divided into eight acute isosceles triangles. There are 1, 4, 23, 180, 1806, 20198, ... (OEIS A056814) ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

A Ferrers diagram represents partitions as patterns of dots, with the nth row having the same number of dots as the nth term in the partition. The spelling "Ferrars" (Skiena ...

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

The fifth of Peano's axioms, which states: If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The number sign # sometimes used in mathematics to indicate the number of a quantity satisfying some condition, e.g., #{n:n>1}. The symbol is also used to denote a primorial.

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

Grinberg constructed a number of small cubic polyhedral graph that are counterexamples to Tait's Hamiltonian graph conjecture (i.e., that every 3-connected cubic graph is ...