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The function lambda(n)=(-1)^(Omega(n)), (1) where Omega(n) is the number of not necessarily distinct prime factors of n, with Omega(1)=0. The values of lambda(n) for n=1, 2, ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

The necker cube is an illusion in which a two-dimensional drawing of an array of cubes appears to simultaneously protrude from and intrude into the page. A Necker cube ...

Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently set of n noncollinear points ...

The Penrose triangle, also called the tribar (Cerf), tri-bar (Ernst 1987), impossible tribar (Pappas 1989, p. 13), or impossible triangle, is an impossible figure published ...

The pentaflake is a fractal with 5-fold symmetry. As illustrated above, five pentagons can be arranged around an identical pentagon to form the first iteration of the ...

The plastic constant P, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio, platin number, Siegel's number, or silver number, is ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

A graph with projective plane crossing number equal to 0 may be said to be projective planar. Examples of projective planar graphs with graph crossing number >=2 include the ...