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Mathematical concept
In mathematics, particularly number theory, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They
Euler_system
physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. These
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Description of the orientation of a rigid body
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They
Euler_angles
Swiss mathematician (1707–1783)
Leonhard Euler (/ˈɔɪlər/ OY-lər; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician
Leonhard_Euler
Second-order partial differential equation describing motion of mechanical system
the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions
Euler–Lagrange_equation
Set of quasilinear hyperbolic equations governing adiabatic and inviscid flow
dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular
Euler equations (fluid dynamics)
Euler_equations_(fluid_dynamics)
Theorem on modular exponentiation
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers
Euler's_theorem
Graphical set representation involving overlapping shapes
An Euler diagram (/ˈɔɪlər/, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining
Euler_diagram
Commercial Linux distribution
EulerOS is a commercial Linux distribution developed by Huawei based on Red Hat Enterprise Linux to provide an operating system for server and cloud environments
EulerOS
Approach to finding numerical solutions of ordinary differential equations
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary
Euler_method
Modification of the Euler method for solving Hamilton's equations
semi-implicit Euler method, also called symplectic Euler, semi-explicit Euler, Euler–Cromer, and Newton–Størmer–Verlet (NSV), is a modification of the Euler method
Semi-implicit_Euler_method
Topics referred to by the same term
Leonhard Euler (1707–1783) was a Swiss mathematician and physicist. Euler may also refer to: Euler (crater), a lunar impact crater in the southern half
Euler_(disambiguation)
2026 scientific priority controversy
himself and partly Levent Alpöge, claiming that their recent advances on Euler equations (a special case of Navier Stokes), reported in the same post,
Navier–Stokes priority controversy
Navier–Stokes_priority_controversy
Euler Mathematical Toolbox (or EuMathT; formerly Euler) is a free and open-source numerical software package. It contains a matrix language, a graphical
Euler_Mathematical_Toolbox
British mathematician who proved Fermat's Last Theorem
related to properties of the Selmer group and use of a tool called an Euler system. Wiles tried and failed for over a year to repair his proof. According
Andrew_Wiles
1995 publication in mathematics
the proof which gave a bound for the order of a particular group: the Euler system used to extend Kolyvagin and Flach's method was incomplete. The error
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
17th-century conjecture proved by Andrew Wiles in 1994
hints of cutting-edge research and new techniques, and discovered an Euler system recently developed by Victor Kolyvagin and Matthias Flach that seemed
Fermat's_Last_Theorem
Curve whose curvature changes linearly
An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the
Euler_spiral
Scientific educational toy
Euler's Disk is a trademarked scientific educational toy used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved
Euler's_Disk
Base of natural logarithms
sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with other numbers named after Euler. Alternatively
E_(mathematical_constant)
Number of integers coprime to and less than n
\ln(x)} or log e ( x ) {\displaystyle \log _{e}(x)} . In number theory, Euler's totient function counts the positive integers up to a given integer n {\displaystyle
Euler's_totient_function
Cuboid whose edges and face diagonals have integer lengths
an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick
Euler_brick
Modular unit in mathematics
quadratic fields of cyclotomic units. They form an example of an Euler system. A system of elliptic units may be constructed for an elliptic curve E with
Elliptic_unit
Line constructed from a triangle
In geometry, the Euler line, named after Leonhard Euler (/ˈɔɪlər/ OY-lər), is a line determined from any triangle that is not equilateral. It is a central
Euler_line
American mathematician (born 1943)
questions in the course of my work on Euler systems, and together with Illusie read critically the Euler system argument. Their questions led to my discovery
Nick_Katz
Group of languages
68–76. Euler (2022), pp. 25–26. Seebold (1998), p. 13. Euler (2022), pp. 238, 243. Euler (2022), p. 243. Robinson (1992). Euler (2013), p. 53. Euler (2022)
West_Germanic_languages
Integers occurring in the coefficients of the Taylor series of 1/cosh t
In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh t = 2 e
Euler_number
Herbrand–Ribet theorem Vandiver's conjecture Stickelberger's theorem Euler system p-adic L-function Arithmetic geometry Complex multiplication Abelian
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Pair in mathematics
mathematics, a Lagrangian system is a pair (Y, L), consisting of a smooth fiber bundle Y → X and a Lagrangian density L, which yields the Euler–Lagrange differential
Lagrangian_system
Used to count, measure, and label
would later be named Euler's number (e). Irrational numbers began to be studied systematically in the 18th century, with Leonhard Euler who proved that the
Number
Russian mathematician (born 1955)
March, 1955) is a Russian mathematician who wrote a series of papers on Euler systems, leading to breakthroughs on the Birch and Swinnerton-Dyer conjecture
Victor_Kolyvagin
Numerical method for ordinary differential equations
numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the
Backward_Euler_method
Diagram that shows all possible logical relations between a collection of sets
as by Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler in 1768 (Letters to a German Princess). The idea was popularised by Venn
Venn_diagram
Method for load calculation in construction
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which
Euler–Bernoulli_beam_theory
American mathematician (born 1956)
astronomer and physicist Judith Young. CEILIDH Torus-based cryptography Euler system Stark conjectures Rubin, Karl (1987). "Tate-Shafarevich groups and L-functions
Karl_Rubin
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field.
Contributions of Leonhard Euler to mathematics
Contributions_of_Leonhard_Euler_to_mathematics
Analytic function in mathematics
In mathematics, the Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ {\displaystyle \zeta } (zeta),
Riemann_zeta_function
Movement with a fixed point is rotation
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the body remains
Euler's_rotation_theorem
Script typeface
implemented with the computer-assisted design system Metafont developed by Knuth. Zapf designed and drew the Euler alphabets in 1980–81 and provided critique
AMS_Euler
Telescope in the La Silla Observatory, Chile
Leonhard Euler Telescope, or the Swiss EULER Telescope, is a national, fully automatic 1.2-metre (47 in) reflecting telescope, built and operated by the
Swiss 1.2-metre Leonhard Euler Telescope
Swiss_1.2-metre_Leonhard_Euler_Telescope
Extend Newton's laws of motion to rigid bodies
In classical mechanics, Euler's laws of motion are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They
Euler's_laws_of_motion
Odd composite number which passes the given congruence
In mathematics, an odd composite integer n is called an Euler pseudoprime to base a, if a and n are coprime, and a ( n − 1 ) / 2 ≡ ± 1 ( mod n ) {\displaystyle
Euler_pseudoprime
Figure skating jump, used as transition in a jump sequence
The Euler is an edge jump in figure skating. The Euler jump was known as the half loop jump in International Skating Union (ISU) regulations prior to the
Euler_jump
Statistical model in quantum mechanics of magnetic materials
critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. It is related to
Quantum_Heisenberg_model
Approaches for approximating solutions to differential equations
the forward Euler and backward Euler methods (see numerical ordinary differential equations) and compare the obtained schemes. Forward Euler method The
Explicit_and_implicit_methods
Property of certain dynamical systems
ellipsoids Harmonic oscillator Integrable Clebsch and Steklov systems in fluids Lagrange, Euler, and Kovalevskaya tops Neumann oscillator Two center Newtonian
Integrable_system
Topics referred to by the same term
In mathematics Euler operators may refer to: Euler–Lagrange differential operators d/dx: see Lagrangian system Cauchy–Euler operators e.g. x·d/dx quantum
Euler_operator
Bayesian numerical integration problems. Victor Kolyvagin introduces Euler systems. Ruth Lawrence publishes a paper on homological representations of the
1990_in_science
Quasilinear first-order ordinary differential equation
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a
Euler's equations (rigid body dynamics)
Euler's_equations_(rigid_body_dynamics)
Force arising in rotating frame of reference
In classical mechanics, the Euler force is the fictitious tangential force that appears when a non-uniformly rotating reference frame is used for analysis
Euler_force
Family of Unix-like operating systems that use the Linux kernel
at least two Linux distributions as qualifying for the Unix trademark, EulerOS and Inspur K-UX. Free software projects, although developed through collaboration
Linux
Loss of one degree of freedom in a three-dimensional, three-gimbal mechanism
rockets. Some coordinate systems in mathematics behave as if they were real gimbals used to measure the angles, notably Euler angles. For cases of three
Gimbal_lock
Computation modulo a fixed integer
(mod m). However, the following is true: If c ≡ d (mod φ(m)), where φ is Euler's totient function, then ac ≡ ad (mod m)—provided that a is coprime with
Modular_arithmetic
Chained intrinsic rotations about body-fixed specific axes
rotations are three chained intrinsic rotations about body-fixed specific axes. Euler rotations and Tait–Bryan rotations are particular cases of the Davenport
Davenport_chained_rotations
Class of partial differential equations
These equations generalize classical mechanical systems, such as rigid body motion and ideal fluid flow (Euler equation), by interpreting their evolution as
Euler–Arnold_equation
Mathematical strategy
Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions. This article explains how to convert between the
Conversion between quaternions and Euler angles
Conversion_between_quaternions_and_Euler_angles
Natural number
this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. Euler used trial division, improving on
2,147,483,647
Czech academic and mathematician (1963–2022)
(1990) "On p-adic height pairings" (1991) Selmer complexes (2006) "The Euler system method for CM points on Shimura curves" (2007) "Eichler-Shimura relations
Jan_Nekovář
Extension of the factorial function
}t^{z-1}e^{-t}\,dt} converges absolutely, and is known as the Euler integral of the second kind. (Euler's integral of the first kind is the beta function.) The
Gamma_function
Position of something in relation to its surroundings
to move the object from a reference placement to its current placement. Euler's rotation theorem shows that in three dimensions any orientation can be
Orientation_(geometry)
Equation used in demography
population growth, probably one of the most important equations is the Euler–Lotka equation. Based on the age demographic of females in the population
Euler–Lotka_equation
Result on the p-parts of the Galois eigenspaces of an ideal class group
of Iwasawa theory. Kolyvagin (1990) later gave a simpler proof using Euler systems. A version of the Gras conjecture applying to ray class groups was later
Gras_conjecture
Biological system in animals and plants for gas exchange
Tables (Seventh ed.). Basle, Switzerland: Ciba-Geigy. pp. 257–258. Von Euler, U.S.; Liljestrand, G. (1946). "Observations on the pulmonary arterial blood
Respiratory_system
Typesetting system
fine-tuned over the years and is now set; but when other fonts, such as AMS Euler, were used by Knuth for the first time, new spacing parameters had to be
TeX
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
relates zeros of continuous vector field on compact differential manifold to Euler characteristic of that manifold. It is named after Henri Poincaré who proved
Poincaré–Hopf_theorem
Mathematical paradox
In mathematics, Cramer's paradox or the Cramer–Euler paradox is the statement that the number of points of intersection of two higher-order curves in
Cramer's_paradox
Family of computer operating systems
Operating System V6.1.2 with SP1 or later certification". Archived from the original on April 8, 2016. The Open Group (September 8, 2016). "Huawei EulerOS 2
Unix
Theorem in algebraic number theory relating p-adic L-functions and ideal class groups
of the Mazur–Wiles theorem by using Thaine's method and Kolyvagin's Euler systems, and later proved other generalizations of the main conjecture for imaginary
Main conjecture of Iwasawa theory
Main_conjecture_of_Iwasawa_theory
Special point on a modular curve in mathematics
Zhang & Zhang 2009). Kolyvagin later used Heegner points to construct Euler systems, and used this to prove much of the Birch–Swinnerton-Dyer conjecture
Heegner_point
Study of objects of arithmetic interest over infinite towers of number fields
more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's Euler systems, described in Lang (1990) and Washington (1997), and later proved other
Iwasawa_theory
Result on the class group of certain number fields, strengthening Ernst Kummer's theorem
Ribet's converse to Herbrand's theorem, a consequence of the theory of Euler systems, can be found in Washington's book on cyclotomic fields. Ribet's methods
Herbrand–Ribet_theorem
Object in the Solar System
A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first
Small_Solar_System_body
Formulation of the principle of stationary action
equations for q(t) (the Euler–Lagrange equations), which may be derived as follows. Let q(t) represent the true evolution of the system between two specified
Hamilton's_principle
Theorem of dynamical systems
} , the integrable system is ( H , L 2 , L 3 ) {\displaystyle (H,\mathbf {L} ^{2},L_{3})} . Integrable tops: The Lagrange, Euler and Kovalevskaya tops
Liouville–Arnold_theorem
Human male external reproductive organ
Saddle River, New Jersey: Pearson Education, Inc. Bleske-Rechek, A. L.; Euler, H. A.; LeBlanc, G. J.; Shackelford, T. K.; Weekes-Shackelford, V. A. (2002)
Human_penis
Formula for 3D vector rotation
In mathematics and mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions. It is based on Rodrigues' rotation formula
Euler–Rodrigues_formula
Number equal to the sum of its proper divisors
Two millennia later, Leonhard Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem. It is not known whether
Perfect_number
Gradual change in the total energy of a closed system over time
computer simulations of mechanical systems, energy drift is the gradual change in the total energy of a closed system over time. According to the laws of
Energy_drift
Method for solving certain nonlinear partial differential equations
difference, multidimensional equations and fractional integrable nonlinear systems. The independent variables are a spatial variable x {\displaystyle x} and
Inverse_scattering_transform
Problem in physics and astronomy
In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other
Euler's_three-body_problem
Branch of mathematics
17th century envisioned the geometria situs and analysis situs. Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably
Topology
Italian-French scientist (1736–1813)
mechanics. In 1766, on the recommendation of Leonhard Euler and d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian Academy
Joseph-Louis_Lagrange
Type of integrable system
In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface
Hitchin_system
Operating system that behaves similarly to Unix
that has been certified, and EulerOS and Inspur K-UX are Linux distributions that have been certified. A few other systems (such as IBM z/OS) earned the
Unix-like
Millennium Prize Problem
Tristan Buckmaster, who had derived a set of closely related results on the Euler equations used in the work. The method used to generate the solution to
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
Triangle center associated with the nine-point circle
triangle's three vertices and its orthocenter. The Euler lines of the four triangles formed by an orthocentric system (a set of four points such that each is the
Nine-point_center
Methods used to find numerical solutions of ordinary differential equations
Euler method (or forward Euler method, in contrast with the backward Euler method, to be described below). The method is named after Leonhard Euler who
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Integrable classical system
mathematical physics, the Garnier integrable system, also known as the classical Gaudin model, is a classical mechanical system discovered by René Garnier in 1917
Garnier_integrable_system
Chinese mathematician
TIAN Honored with the Morningside Medal of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, retrieved 2015-05-06.
Tian_Ye_(mathematician)
Influence on an oscillating physical system which reduces or prevents its oscillation
physical systems, damping is the loss of energy of an oscillating system by dissipation. Damping is an influence within or upon an oscillatory system that
Damping
Expression which is not assigned an interpretation
number. Mathematicians, including Gerolamo Cardano, John Wallis, Leonhard Euler, and Carl Friedrich Gauss, explored formal definitions for the square roots
Undefined_(mathematics)
Study of the effects of forces on undeformable bodies
dynamics Multibody system Polhode Herpolhode Precession Poinsot's ellipsoid Gyroscope Physics engine Physics processing unit Euler's Equation B. Paul,
Rigid_body_dynamics
Letters written from Euler to a German princess
mathematician Leonhard Euler between 1760 and 1762 addressed to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise. Euler started the first
Letters_to_a_German_Princess
considered the founder of mountaineering Franc 20 Fr. obverse 1979–2000 Leonhard Euler 1707–1783 mathematician, physicist Franc 10 Fr. obverse 1979–2000 Auguste-Henri
List_of_people_on_banknotes
Wobble of the axis of rotation
the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation (after Leonhard Euler). A pure
Nutation
Country primarily in Western Europe
Country profile: France Archived 1 October 2020 at the Wayback Machine, Euler Hermes "These are the top 10 manufacturing countries in the world". World
France
Equations of motion for viscous fluids
term—hence describing viscous flow. The Navier–Stokes equations generalize the Euler equations which only consider inviscid flow. The Navier–Stokes equations
Navier–Stokes_equations
Graduate-level textbooks in mathematics
Equations Demetrios Christodoulou 1999-12-28 328 978-0691049571 147 Euler Systems Karl Rubin 2000-05-01 240 978-0691050768 148 Triangulated Categories
Annals_of_Mathematics_Studies
Mathematical expression with disputed status
branch of log z defined at z = 0, let alone in a neighborhood of 0. In 1752, Euler in Introductio in analysin infinitorum wrote that a0 = 1 and explicitly
Zero_to_the_power_of_zero
EulerOS NestOS - open-source cloud based operating system based on EulerOS, contributed by openEuler community NuttX - a Unix/Linux-like RTOS for Microcontrollers)
List_of_operating_systems
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