- List of topics named after Leonhard Euler
In

mathematics andphysics , there are a**large**number of topics named in honour ofLeonhard Euler (pronounced**"Oiler**"). As well, many of these topics include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Unfortunately however, many of these entities have been given simple (and otherwise quite ambiguous) names like**Euler's function**,**Euler's equation**, and**Euler's formula**, which are further confused by variations of the "Euler"-prefix (and then, may still refer to the same thing anyway.) Overall though, 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". Fact|date=October 2007**General "Euler-" mathematical topics***

Euler angles defining a rotation in space.

*Euler approximation - (seeEuler method )

*Euler brick

*Euler characteristic inalgebraic topology andtopological graph theory , and the corresponding Euler's formula $scriptstyle\; chi(S^2),=,F,-,E,+,V,=,2.$

*Euler circle

*Eulerian circuit - (seeEulerian path )

*Euler class

*Euler's constant - (seeEuler-Mascheroni constant orEuler's number )

*Euler cycle - (seeEulerian path )

*Euler's criterion - quadratic residues modulo primes

*Euler derivative (as opposed toLagrangian derivative )

*Euler diagram - likely better (but wrongly) known as "Venn diagram " (which has more restrictions)

*Euler's disk - a circular disk that spins, without slipping, on a surface

*Eulerian graph - (seeEulerian path )

*TheEuler integral s of the first and second kind, namely thebeta function andgamma function .

*Euler's line - relation betweentriangle center s

*Euler-Mascheroni constant or "Euler's constant" γ ≈ 0.577216

*Euler's number , e, the base of thenatural logarithm .

*Euler operator - set of functions to createpolygon mesh es

*Euler parameters - (seeEuler-Rodrigues parameters )

*Eulerian path , a path through a graph that takes each edge once.

*Euler polynomials

*Euler pseudoprime

*Euler-Rodrigues parameters - ConcernsLie group s andquaternions

*Euler's rule - findingamicable numbers

*Euler spline - composed of classical Euler polynomial arcs (cred. to [*http://pages.cs.wisc.edu/~deboor/HAT/fpapers/isobib.pdf Schoenberg, 1973 - PDF*] )

*Euler squares, usually calledGraeco-Latin square s.

*Euler summation

*Euler system , a collection of cohomology classes.

*Euler's three-body problem (See also:#Other things named after Euler )**Euler—conjectures***

Euler's conjecture (Waring's problem)

*Euler's sum of powers conjecture (Also see here.)**Euler—equations***Euler's equation - usually refers to

Euler's equations (rigid body dynamics) ,Euler's formula ,Euler's homogeneous function theorem , orEuler's identity

*Euler equations (fluid dynamics) influid dynamics .

*Euler's equations (rigid body dynamics) , concerning the rotations of arigid 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**Euler—formulas***

Euler's formula $e^\{i\; x\}=cos\{x\}\; +isin\{x\}$ incomplex analysis .

*Euler's formula for planar graphs: "v" − "e" + "f" = 2

*Euler's continued fraction formula

*Euler product formula - for theRiemann zeta function .

*Euler's summation formula , a theorem about integrals.

*Euler–Maclaurin formula - relation between integrals and sums

*Euler–Rodrigues formulas - concernsEuler-Rodrigues parameters and 3D rotation matrices**Euler—functions***The

Euler function , amodular form that is a prototypicalq-series .

*Euler's homogeneous function theorem

*Euler's totient function (or Euler phi (φ) function) innumber theory , counting the number of coprime integers less than an integer.**Euler—identities***

Euler's identity $e^\{ipi\}+1\; =\; 0$.

*"Euler's identity" may also refer to thepentagonal number theorem .**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 number s are aninteger sequence .

*Eulerian number s are another integer sequence.

*Euler number (physics) , the cavitation number influid dynamics .

*Euler number (topology) - now, Euler characteristic

*Lucky numbers of Euler **Euler—theorems***

Euler's homogeneous function theorem , a theorem abouthomogeneous polynomial s.

*Euler's infinite tetration theorem

*Euler's rotation theorem

*Euler's theorem (differential geometry) on the existence of theprincipal curvatures of asurface and orthogonality of the associated principal directions.

*Euler's theorem in geometry , relating thecircumcircle andincircle of atriangle .

*Euclid-Euler theorem

*Euler-Fermat theorem , that $a^\{phi(m)\}=1\; pmod\; m$ whenever "a" iscoprime to "m", and φ is the totient function.**Other things named after Euler***

2002 Euler (an asteroid)

*Euler Medal , a prize for research incombinatorics

*Euler programming language

*Euler (software)

*AMS Euler typeface**Topics by field of study**Selected topics from above, grouped by subject.

**Derivatives and integrals***Euler approximation - (see

Euler's method )

*Euler derivative (as opposed toLagrangian derivative )

*TheEuler integral s of the first and second kind, namely thebeta function andgamma function .

*TheEuler 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**Geometry and spatial arrangement***

Euler angles defining a rotation in space.

*Euler brick

*Euler's line - relation betweentriangle center s

*Euler operator - set of functions to createpolygon meshes

*Euler's rotation theorem

*Euler squares, usually calledGraeco-Latin square s.

*Euler's theorem in geometry , relating thecircumcircle andincircle of atriangle .

*Euler–Rodrigues formulas - concernsEuler-Rodrigues parameters and 3D rotation matrices**Graph theory***

Euler characteristic inalgebraic topology andtopological graph theory , and the corresponding Euler's formula $scriptstyle\; chi(S^2)=F-E+V=2.$

*Eulerian circuit - (seeEulerian path )

*Euler class

*Euler cycle - (seeEulerian 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 - (seeEulerian path )

*Euler number (topology) - now, Euler characteristic

*Eulerian path , a path through a graph that takes each edge once.**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**Physical systems***

Euler's disk - a circular disk that spins, without slipping, on a surface

*Euler equations influid dynamics .

*Euler's equations , concerning the rotations of arigid body .

*Euler number (physics) , the cavitation number influid 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**Polynomials***

Euler's homogeneous function theorem , a theorem abouthomogeneous polynomial s.

*Euler polynomials

*Euler spline - composed of classical Euler polynomial arcs (cred. to [*http://pages.cs.wisc.edu/~deboor/HAT/fpapers/isobib.pdf Schoenberg, 1973 - PDF*] )**Prime numbers***

Euler's criterion - quadratic residues modulo by primes

*Euler product -infinite product expansion, indexed by prime numbers of aDirichlet series

*Euler pseudoprime

*Euler's totient function (or Euler phi (φ) function) innumber theory , counting the number of coprime integers less than an integer.**ee also***

Contributions of Leonhard Euler to mathematics

*Euler on infinite series

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