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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
mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique
List of topics named after Leonhard Euler
List_of_topics_named_after_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
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
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)
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
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
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
Scientific educational toy
Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, is a trademarked scientific educational toy. It is used to illustrate and study the dynamic
Euler's_Disk
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
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)
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
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
2.71828...; base of natural logarithms
sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,
E_(mathematical_constant)
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
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
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_numbers
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
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
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
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
American mathematician
astronomer and physicist Judith Young. CEILIDH Torus-based cryptography Euler system Stark conjectures Rubin, Karl (1987). "Tate-Shafarevich groups and L-functions
Karl_Rubin
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
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
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
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
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
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
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
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
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
Stony background asteroid from the inner regions of the asteroid belt
2002 Euler is a stony background asteroid from the inner regions of the asteroid belt, approximately 17 kilometers (11 miles) in diameter. It was discovered
2002_Euler
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
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
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
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)
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
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
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
Extend Newton's laws of motion to rigid bodies
motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws. Euler's first law states that the rate of change
Euler's_laws_of_motion
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
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
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
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
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
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
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
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
Crater on the Moon
Euler is a lunar impact crater located in the southern half of the Mare Imbrium, and is named after the Swiss mathematician, physicist and astronomer
Euler_(crater)
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
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)
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
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
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
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)
Polish mathematician
part of programs on perfectoid spaces, the homological conjectures and Euler systems, respectively. She moved to France in 2012 as a directrice de recherches
Wiesława_Nizioł
Bayesian numerical integration problems. Victor Kolyvagin introduces Euler systems. Ruth Lawrence publishes a paper on homological representations of the
1990_in_science
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
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
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
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
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
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
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
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
Differential calculus on function spaces
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such
Calculus_of_variations
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
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
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
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
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
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
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
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
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
4 planar points which are all orthocenters of triangles formed by the other 3
diagram adjacent. The four Euler lines of an orthocentric system are orthogonal to the four orthic axes of an orthocentric system. The six connectors that
Orthocentric_system
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
Number divisible only by 1 and itself
the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be
Prime_number
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
is the Euler characteristic of M {\displaystyle M} . A particularly useful corollary is when there is a non-vanishing vector field implying Euler characteristic
Poincaré–Hopf_theorem
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
Geometric model of the physical space
intrinsic coordinate systems on a surface, beginning the theory of intrinsic geometry upon which modern geometric ideas are based. In 1760, Euler proved a theorem
Three-dimensional_space
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
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
Ways to represent 3D rotations
placement in space. According to Euler's rotation theorem, the rotation of a rigid body (or three-dimensional coordinate system with a fixed origin) is described
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Method for specifying point positions
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points
Coordinate_system
Swedish physiologist and pharmacologist (1905–1983)
neurotransmitters. Ulf Svante von Euler-Chelpin was born in Stockholm, the son of two noted scientists, Hans von Euler-Chelpin, a professor of chemistry
Ulf_von_Euler
German algebraic number theorist
their work in number theory, in particular for their discovery of a new Euler system, and for their applications of this to generalisations of the Birch–Swinnerton-Dyer
Sarah_Zerbes
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
Concept in classical mechanics
the Coriolis force, and, for non-uniformly rotating reference frames, the Euler force. Scientists in a rotating box can measure the rotation speed and axis
Rotating_reference_frame
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
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
Country in South Asia
most certainly I have never met his equal, and I can compare him only with Euler and Jacobi. He worked, far more than the majority of modern mathematicians
India
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
Tool to study dynamic behavior of interconnected rigid or flexible bodies
simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies
Multibody_system
The following is a list of Solar System objects by orbit, ordered by increasing distance from the Sun. Most named objects in this list have a diameter
List_of_Solar_System_objects
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
Odd composite number which passes the given congruence
In number theory, an odd integer n is called an Euler–Jacobi probable prime (or, more commonly, an Euler probable prime) to base a, if a and n are coprime
Euler–Jacobi_pseudoprime
Formulation of classical mechanics using momenta
({\boldsymbol {p}},{\boldsymbol {q}})} , the ( n {\displaystyle n} -dimensional) Euler–Lagrange equation ∂ L ∂ q − d d t ∂ L ∂ q ˙ = 0 {\displaystyle {\frac {\partial
Hamiltonian_mechanics
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