"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 $\scriptstyle \chi (S^{2})\,=\,F\,-\,E\,+\,V\,=\,2.$
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 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 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

Congettura di Eulero

Congettura di Eulero (somma di potenze)
Congettura di Eulero sui quadrati greco-latini
Congettura di Eulero legata al problema di Waring

Equazioni di Eulero

Formula di Eulero

Formula di Eulero: $e^{ix}=\cos {x}+i\sin {x}$
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
Euler's homogeneous function theorem ----------------
Funzione φ di Eulero

Identità di Eulero

Identità di Eulero: $e^{i\pi }+1=0$
A volte è riferita al teorema dei numeri pentagonali

Numeri di Eulero

La costante 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—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 $a^{\phi (m)}=1{\pmod {m}}$ whenever a is coprime to m, and φ is the 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 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

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

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.

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 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

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)

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.

[[cs:Seznam pojmů pojmenovaných po Leonhardu Eulerovi]] [[de:Leonhard Euler#Nach_Euler_Benanntes]] [[ru:Список объектов, названных в честь Леонарда Эйлера]]

Utente:Dr Zimbu/Sandbox4

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