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= "Oggetti" che prendono il nome da Eulero =

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'''.

==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 <math>\scriptstyle \chi(S^2)\,=\,F\,-\,E\,+\,V\,=\,2.</math>

*[[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 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]] - (see [[Eulerian path]])

*The [[Euler integral]]s of the first and second kind, namely the [[beta function]] and [[gamma function]].

*[[Euler's line]] - relation between [[triangle center]]s

*[[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 mesh]]es

*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 group]]s and [[quaternions]]

*[[Euler's rule]] - finding [[amicable 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 called [[Graeco-Latin square]]s.

*[[Euler summation]]

*[[Euler system]], a collection of cohomology classes.

*[[Euler's three-body problem]]

(See also: [[#Other things named after Euler]])

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Editor's Note: "Euler-xxxx" reinforces the idea that entries have both "Euler" and "xxxx" IN THEIR NAME, whereas "Euler xxxx" just shows that entries are *related* to both "Euler" and "xxxx" -->

== Congettura di Eulero ==

*[[Congettura di Eulero]] (somma di potenze)

*[[Quadrato greco-latino|Congettura di Eulero]] sui quadrati greco-latini

*[[Problema di Waring|Congettura di Eulero]] legata al problema di Waring

== Equazioni di Eulero ==

*[[Equazioni di Eulero]] (fluidodinamica)

*[[Equazioni di Eulero (dinamica del corpo rigido)]]

*[[Teoria della trave|Equazioni di Eulero-Bernoulli]]

*[[Equazione di Eulero-Cauchy]]

*[[Equazione di Eulero-Lagrange]]

*[[Equazione di Eulero-Poisson-Draboux]]

*[[Equazione di Eulero-Tricomi]]

== Formula di Eulero ==

*[[Formula di Eulero]]: <math>e^{i x}=\cos{x} +i\sin{x}</math>

*[[Grafo planare|Formula di Eulero]] per i grafi planari

*[[Formula per le frazioni continue di Eulero]]

*[[Prodotto di Eulero]]

*[[Formula di Eulero-Maclaurin]]

*[[Formule di Eulero-Rodrigues]]

== Funzioni di Eulero ==

*[[Funzione di Eulero]], una [[forma modulare]]

*[[homogeneous function|Euler's homogeneous function theorem]] ----------------

*[[Funzione φ di Eulero]]

== Identità di Eulero ==

*[[Identità di Eulero]]: <math>e^{i\pi}+1 = 0</math>

*A volte è riferita al [[teorema dei numeri pentagonali]]

== Numeri di Eulero ==

*La costante [[e (costante matematica)|''e'']] è a volte detta numero di Eulero

*[[Euler's idoneal numbers]] ------------------

*[[Numeri di Eulero]]

*[[Numeri euleriani]]

*Numero di Eulero, in [[topologia]], è a volte la [[caratteristica di Eulero]]

*[[Lucky numbers of Euler]] ------------------

==Euler&mdash;theorems==

*[[Euler's homogeneous function theorem]], a theorem about [[homogeneous polynomial]]s.

*[[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]].

*[[perfect number|Euclid-Euler theorem]]

*[[Euler-Fermat theorem]], that <math>a^{\phi(m)}=1 \pmod m</math> whenever ''a'' is [[coprime]] to ''m'', and φ is the [[Euler's totient function|totient function]].

==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]]

==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 to [[Lagrangian derivative]])

*The [[Euler integral]]s 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.

*[[Cauchy-Euler equation|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 between [[triangle center]]s

*[[Euler operator]] - set of functions to create [[polygon meshes]]

*[[Euler's rotation theorem]]

*Euler squares, usually called [[Graeco-Latin square]]s.

*[[Euler's theorem in geometry]], relating the [[circumcircle]] and [[incircle]] of a [[triangle]].

*[[Euler–Rodrigues formulas]] - concerns [[Euler-Rodrigues parameters]] and 3D rotation matrices

===Graph theory===

*[[Euler characteristic]] in [[algebraic topology]] and [[topological graph theory]], and the corresponding Euler's formula <math>\scriptstyle \chi(S^2)=F-E+V=2.</math>

*[[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)

*[[Planar graph#Euler's formula|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.

===Logarithms===

*[[e (mathematical constant)|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 (fluid dynamics)|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&ndash;Bernoulli beam equation]], concerning the elasticity of structural beams.

*[[buckling|Euler formula]] in calculating the buckling load of columns.

*[[Euler-Tricomi equation]] - concerns transonic flow

===Polynomials===

*[[Euler's homogeneous function theorem]], a theorem about [[homogeneous 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 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.

<nowiki>

[[cs:Seznam pojmů pojmenovaných po Leonhardu Eulerovi]]

[[de:Leonhard Euler#Nach_Euler_Benanntes]]

[[ru:Список объектов, названных в честь Леонарда Эйлера]] </nowiki>