to the pentagonal number theorem. Numbers Euler's number, , the base of the natural logarithm Euler's idoneal numbers, a set of 65 or possibly 66 or 67 integers with special properties Eulerian numbers count certain types of permutations. Euler number (physics), the cavitation number in fluid dynamics. Euler number (algebraic topology) – now, Euler characteristic, classically the number of vertices minus edges plus faces of a polyhedron. Euler number (3-manifold topology) – see Seifert fiber space Lucky numbers of Euler Euler's constant gamma (γ), also known as the Euler–Mascheroni constant Eulerian integers, more commonly called Eisenstein integers, the algebraic integers of form where is a complex cube root of 1. Euler–Gompertz constant Theorems Laws Euler's first law, the linear momentum of a body is equal to the product of the mass of the body and the velocity of its center of mass. Euler's second law, the sum of the external moments about a point is equal to the rate of change of angular momentum about that point. Other things Topics by field of study Selected topics from above, grouped by subject, and additional topics from the fields of music and physical systems Analysis: derivatives, integrals, and logarithms Geometry and spatial arrangement Graph theory Euler characteristic (formerly called Euler number) in algebraic topology and topological graph theory, and the corresponding Euler's formula Eulerian circuit, Euler cycle or Eulerian path – a path through a graph that takes each edge once Eulerian graph has all its vertices spanned by an Eulerian path Euler class Euler diagram – incorrectly, but more popularly, known as Venn diagrams, its subclass Euler tour technique Music Euler–Fokker genus Euler's tritone Number theory Euler's criterion – quadratic residues modulo by primes Euler product – infinite product expansion, indexed by prime numbers of a Dirichlet series Euler pseudoprime Euler–Jacobi pseudoprime Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer. Euler system Euler's factorization method Physical systems Polynomials Euler's homogeneous function theorem, a theorem about homogeneous polynomials. Euler polynomials Euler spline – splines composed of arcs using Euler polynomials See also Contributions of Leonhard Euler to mathematics Notes Euler Leonhard Euler