List of topics named after Leonhard Euler

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In mathematics and physics, there is a large number of topics named in honor of Leonhard Euler, many of which include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Unfortunately, many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula.

Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. Physicists and mathematicians sometimes jest that, in an effort to avoid naming everything after Euler, discoveries and theorems are named after the "first person after Euler to discover it".^[1]^[2]

[edit] General "Euler-" mathematical topics

Euler angles defining a rotation in space.
Euler approximation - (see Euler method)
Euler brick
Euler characteristic in algebraic topology and topological graph theory, and the corresponding Euler's formula $\scriptstyle \chi(S^2)\,=\,F\,-\,E\,+\,V\,=\,2.$
Euler circle
Eulerian circuit - (see Eulerian path)
Euler class
Euler's constant - (see Euler-Mascheroni constant or Euler's number)
Euler cycle - (see Eulerian path)
Euler's criterion - quadratic residues modulo primes
Euler derivative (as opposed to Lagrangian derivative)
Euler diagram - likely more widely (though incorrectly) known as Venn diagram (which has more restrictions)
Euler's disk - a circular disk that spins, without slipping, on a surface
Eulerian graph - (see Eulerian path)
The Euler integrals of the first and second kind, namely the beta function and gamma function.
Euler's line - relation between triangle centers
Euler-Mascheroni constant or Euler's constant γ ≈ 0.577216
Euler's number, e, the base of the natural logarithm.
Euler operator - set of functions to create polygon meshes
Euler parameters - (see Euler-Rodrigues parameters)
Eulerian path, a path through a graph that takes each edge once.
Euler polynomials
Euler pseudoprime
Euler-Rodrigues parameters - Concerns Lie groups and quaternions
Euler's rule - finding amicable numbers
Euler spline - composed of classical Euler polynomial arcs (cred. to Schoenberg, 1973 - PDF)
Euler squares, usually called Graeco-Latin squares.
Euler summation
Euler system, a collection of cohomology classes.
Euler's three-body problem

[edit] Euler—conjectures

(Also see Euler's conjecture.)

[edit] Euler—equations

Euler's equation - usually refers to Euler's equations (rigid body dynamics), Euler's formula, Euler's homogeneous function theorem, or Euler's identity
Euler equations (fluid dynamics) in fluid dynamics.
Euler's equations (rigid body dynamics), concerning the rotations of a rigid body.
Euler-Bernoulli beam equation, concerning the elasticity of structural beams.
Euler-Cauchy equation (or Euler Equation), a second-order linear differential equation
Euler-Lagrange equation (in regard to minimization problems)
Euler–Poisson–Darboux equation
Euler-Tricomi equation - concerns transonic flow
Binomial_transform#Euler_transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series

[edit] Euler—formulas

Euler's formula $e i x = cos x + i sin x$ in complex analysis.
Euler's formula for planar graphs: v − e + f = 2
Euler's continued fraction formula
Euler product formula - for the Riemann zeta function.
Euler's summation formula, a theorem about integrals.
Euler–Maclaurin formula - relation between integrals and sums
Euler–Rodrigues formulas - concerns Euler–Rodrigues parameters and 3D rotation matrices

[edit] Euler—functions

The Euler function, a modular form that is a prototypical q-series.
Euler's homogeneous function theorem
Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer.

[edit] Euler—identities

Euler's identity $e i π + 1 = 0$ .
Euler's four-square identity, which shows that the product of two sums of four squares can itself be expressed as the sum of four squares.
Euler's identity may also refer to the pentagonal number theorem.

[edit] Euler—numbers

Euler's number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant.
Euler's idoneal numbers
Euler numbers are an integer sequence.
Eulerian numbers are another integer sequence.
Euler number (physics), the cavitation number in fluid dynamics.
Euler number (topology) - now, Euler characteristic
Lucky numbers of Euler

[edit] Euler—theorems

Euler's homogeneous function theorem, a theorem about homogeneous polynomials.
Euler's infinite tetration theorem
Euler's rotation theorem
Euler's theorem (differential geometry) on the existence of the principal curvatures of a surface and orthogonality of the associated principal directions.
Euler's theorem in geometry, relating the circumcircle and incircle of a triangle.
Euclid-Euler theorem
Euler-Fermat theorem, that $a φ(m) = 1(mod m)$ whenever a is coprime to m, and φ is the totient function.

[edit] Euler—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.

[edit] Other things named after Euler

2002 Euler (an asteroid)
Euler Medal, a prize for research in combinatorics
Euler programming language
Euler (software)
AMS Euler typeface
Project Euler

[edit] Topics by field of study

Selected topics from above, grouped by subject.

[edit] Derivatives and integrals

Euler approximation - (see Euler's method)
Euler derivative (as opposed to Lagrangian derivative)
The Euler integrals of the first and second kind, namely the beta function and gamma function.
The Euler method, a method for finding numerical solutions of differential equations
Euler's summation formula, a theorem about integrals.
Euler-Cauchy equation (or Euler Equation), a second-order linear differential equation
Euler-Maclaurin formula - relation between integrals and sums

[edit] Geometry and spatial arrangement

Euler angles defining a rotation in space.
Euler brick
Euler's line - relation between triangle centers
Euler operator - set of functions to create polygon meshes
Euler's rotation theorem
Euler squares, usually called Graeco-Latin squares.
Euler's theorem in geometry, relating the circumcircle and incircle of a triangle.
Euler–Rodrigues formulas - concerns Euler-Rodrigues parameters and 3D rotation matrices

[edit] Graph theory

Euler characteristic in algebraic topology and topological graph theory, and the corresponding Euler's formula $\scriptstyle \chi(S^2)=F-E+V=2.$
Eulerian circuit - (see Eulerian path)
Euler class
Euler cycle - (see Eulerian path)
Euler diagram - likely better (but wrongly) known as Venn diagram (which has more restrictions)
Euler's formula for planar graphs: v − e + f = 2
Eulerian graph - (see Eulerian path)
Euler number (topology) - now, Euler characteristic
Eulerian path, a path through a graph that takes each edge once.

[edit] Logarithms

Euler's number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant.
Euler-Mascheroni constant or Euler's constant γ ≈ 0.577216

[edit] Physical systems

Euler's disk - a circular disk that spins, without slipping, on a surface
Euler equations in fluid dynamics.
Euler's equations, concerning the rotations of a rigid body.
Euler number (physics), the cavitation number in fluid dynamics.
Euler's three-body problem
Euler–Bernoulli beam equation, concerning the elasticity of structural beams.
Euler formula in calculating the buckling load of columns.
Euler-Tricomi equation - concerns transonic flow

[edit] Polynomials

Euler's homogeneous function theorem, a theorem about homogeneous polynomials.
Euler polynomials
Euler spline - composed of classical Euler polynomial arcs (cred. to Schoenberg, 1973 - PDF)

[edit] Prime numbers

Euler's criterion - quadratic residues modulo by primes
Euler product - infinite product expansion, indexed by prime numbers of a Dirichlet series
Euler pseudoprime
Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer.

[edit] See also

[edit] Notes

^ David S. Richeson (2008), Euler's Gem: The Polyhedron Formula and the Birth of Topology (illustrated ed.), Princeton University Press, p. 86, ISBN 9780691126777, http://books.google.com/books?id=LB_6VogerHIC&pg=PA86&dq=%22person+after+Euler%22
^ C. H. Edwards; David E. Penney (2004), Differential equations and boundary value problems :, 清华大学出版社, p. 443, ISBN 9787302099789, http://books.google.com/books?id=51KTl4Fmh2wC&pg=PA443&dq=%22person+after+Euler%22

[0] David S. Richeson (2008), Euler's Gem: The Polyhedron Formula and the Birth of Topology (illustrated ed.), Princeton University Press, p. 86, ISBN 9780691126777, http://books.google.com/books?id=LB_6VogerHIC&pg=PA86&dq=%22person+after+Euler%22

[1] C. H. Edwards; David E. Penney (2004), Differential equations and boundary value problems :, 清华大学出版社, p. 443, ISBN 9787302099789, http://books.google.com/books?id=51KTl4Fmh2wC&pg=PA443&dq=%22person+after+Euler%22

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