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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
and 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
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His
Contributions of Leonhard Euler to mathematics
Contributions_of_Leonhard_Euler_to_mathematics
Swiss mathematician and astronomer (1734–1800)
contributions to electrostatics. The eldest son of the renowned mathematician Leonhard Euler, he served as professor of physics at the Imperial Academy of Sciences
Johann_Euler
Ongoing project compiling Leonhard Euler's scientific writings
Opera Omnia Leonhard Euler (Leonhardi Euleri Opera omnia) is the compilation of Leonhard Euler's scientific writings. The project of this compilation was
Opera_Omnia_Leonhard_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
Difference between logarithm and harmonic series
constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled De Progressionibus harmonicis observationes (Observations on
Euler's_constant
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
Graphical set representation involving overlapping shapes
relations between different sets, the Euler diagram shows only relevant relationships. The Swiss mathematician Leonhard Euler (1707–1783) is one of the most
Euler_diagram
Approach to finding numerical solutions of ordinary differential equations
The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1770). The Euler method
Euler_method
Method for load calculation in construction
rotating about an axis that intersects the extreme compression fiber. Leonhard Euler built on Jacob Bernoulli's work, and applied differential calculus to
Euler–Bernoulli_beam_theory
Complex exponential in terms of sine and cosine
is named after Leonhard Euler, who mentioned the formula in his influential 1748 treatise Introductio in analysin infinitorum. Euler's formula states
Euler's_formula
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
Landmark mathematics textbook by Leonhard Euler
Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler around 1765 in German. It was first published in Russian as "Universal
Elements_of_Algebra
Number of integers coprime to and less than n
/n\mathbb {Z} } ). It is also used for defining the RSA encryption system. Leonhard Euler introduced the function in 1763. However, he did not at that time choose
Euler's_totient_function
Website and series of mathematical challenges
Project Euler (named after Leonhard Euler) is a website dedicated to a series of computational problems intended to be solved with computer programs.
Project_Euler
Scientific educational toy
several scientific papers. Bendik named the toy after mathematician Leonhard Euler. Joseph Bendik first noted the interesting motion of the spinning disk
Euler's_Disk
German mathematician (1690–1764)
and the Goldbach–Euler theorem. He had a close friendship with famous mathematician Leonhard Euler, serving as inspiration for Euler's mathematical pursuits
Christian_Goldbach
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)
Analytic function in mathematics
applications in physics, probability theory, and applied statistics. Leonhard Euler first introduced and studied the function over the reals in the first
Riemann_zeta_function
Summation formula
consequence. The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735. Euler needed it to compute slowly converging infinite
Euler–Maclaurin_formula
Disproved conjecture in number theory
In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was presented by Leonhard Euler in 1778 to the Academy
Euler's sum of powers conjecture
Euler's_sum_of_powers_conjecture
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)
Turbomachinery Equation in Fluid Dynamics
determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century. These equations can be derived from the moment
Euler's pump and turbine equation
Euler's_pump_and_turbine_equation
Swedish scientist (1873–1964)
Institute for organic-chemical research (1938–1948). Euler-Chelpin was distantly related to Leonhard Euler. He married chemist Astrid Cleve, the daughter of
Hans_von_Euler-Chelpin
Mathematical concept
are all members of the larger set of prime generating polynomials. Leonhard Euler published the polynomial k2 − k + 41 which produces prime numbers for
Lucky_numbers_of_Euler
Theorem on modular exponentiation
denotes Euler's totient function; that is a φ ( n ) ≡ 1 ( mod n ) . {\displaystyle a^{\varphi (n)}\equiv 1{\pmod {n}}.} In 1736, Leonhard Euler published
Euler's_theorem
Mathematical equation linking e, i and π
circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula e i x = cos x
Euler's_identity
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
Quasilinear first-order ordinary differential equation
the body. They are named in honour of Leonhard Euler. In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity
Euler's equations (rigid body dynamics)
Euler's_equations_(rigid_body_dynamics)
Use of a Dirichlet series expansion to calculate the complex function
Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis Variae observationes circa series infinitas (Various Observations
Proof of the Euler product formula for the Riemann zeta function
Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function
Topological invariant in mathematics
solids in 1537 in an unpublished manuscript by Francesco Maurolico. Leonhard Euler, for whom the concept is named, introduced it for convex polyhedra more
Euler_characteristic
(Vortrag) and a musical program supporting the event. The Euler Lecture is named in honor of Leonhard Euler, who spent the years from 1741 to 1766 in Berlin and
Euler_Lecture
Characteristic class of oriented, real vector bundles
manifold, it generalizes the classical notion of Euler characteristic. It is named after Leonhard Euler because of this. Throughout this article E {\displaystyle
Euler_class
Diagram that shows all possible logical relations between a collection of sets
such 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_diagram
Parameter in fluid flow calculations
formulated number with different meaning List of topics named after Leonhard Euler Shah and Sekulic, Fundamentals of Heat Exchanger Design, John Wiley
Euler_number_(physics)
Book by Leonhard Euler
work published by mathematician Leonhard Euler which describes analytically the mathematics governing movement. Euler both developed the techniques of
Mechanica
Equation used in demography
earlier work of Leonhard Euler. The Euler–Lotka equation, derived and discussed below, is often attributed to either of its origins: Euler, who derived a
Euler–Lotka_equation
Formula to quantify column buckling under a given load
factor This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. The column will remain straight for loads less than the critical load
Euler's_critical_load
Extension of the factorial function
well defined for real values of x other than the negative integers. Leonhard Euler later gave two different definitions: the first was not his integral
Gamma_function
Trail in a graph that visits each edge once
that starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736
Eulerian_path
Classic problem in graph theory
once. Its mathematical formalization and proof of impossibility by Leonhard Euler, in 1736, laid the foundations of graph theory and foreshadowed the
Seven_Bridges_of_Königsberg
Formula concerning prime numbers
a^{\tfrac {p-1}{2}}{\pmod {p}}.} The criterion dates from a 1748 paper by Leonhard Euler. The proof uses the fact that the residue classes modulo a prime number
Euler's_criterion
Mathematical function
0 {\displaystyle \Re (z_{2})>0} . The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its
Beta_function
Branch of mathematics
the 17th century envisioned the geometria situs and analysis situs. Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably
Topology
Leonhard Euler Gold Medal (Золотая медаль имени Леонарда Эйлера) is a medal named after the Swiss, German, and Russian mathematician Leonhard Euler,
Leonhard_Euler_Gold_Medal
Natural number
of 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
2,147,483,647
Mathematical method in graph theory
The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph
Euler_tour_technique
Complex number whose mapping on a coordinate plane produces a triangular lattice
Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form z = a + b ω , {\displaystyle z=a+b\omega
Eisenstein_integer
Script typeface
Euler digitization project as his M.S. thesis in 1985. The AMS Euler typeface is named after Leonhard Euler. First implemented in METAFONT, AMS Euler
AMS_Euler
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
Letters_to_a_German_Princess
Orthogonality of the directions of the principal curvatures of a surface
curves the most and the least. The theorem is named for Leonhard Euler who proved the theorem in (Euler 1760). More precisely, let M be a surface in three-dimensional
Euler's theorem (differential geometry)
Euler's_theorem_(differential_geometry)
Integers occurring in the coefficients of the Taylor series of 1/cosh t
Bernoulli number Dirichlet beta function Euler–Mascheroni constant List of topics named after Leonhard Euler Jha, Sumit Kumar (2019). "A new explicit
Euler_number
Annual mathematics book award
The Euler Book Prize is an award named after Swiss mathematician and physicist Leonhard Euler (1707–1783) and given annually at the Joint Mathematics
Euler_Book_Prize
Extend Newton's laws of motion to rigid bodies
body 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
Second-order partial differential equation describing motion of mechanical system
mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange
Euler–Lagrange_equation
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)
Italian-French scientist (1736–1813)
celestial mechanics. In 1766, on the recommendation of Leonhard Euler and d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian
Joseph-Louis_Lagrange
Vector formula for a rotation in space, given its axis
so(3) to its Lie group SO(3). This formula is variously credited to Leonhard Euler, Olinde Rodrigues, or a combination of the two. A detailed historical
Rodrigues'_rotation_formula
Polynomial sequence
the previous element (permutations with k {\textstyle k} "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones
Eulerian_number
Exponent of a power of two
the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives
Binary_logarithm
German physicist
a direct descendant of renowned Swiss mathematician Leonhard Euler. [citation needed] Hans Euler, "Über die Streuung von Licht an Licht nach der Diracschen
Hans_Heinrich_Euler
Even integers as sums of two primes
1742, the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture: Every
Goldbach's_conjecture
Method in Itô calculus
an extension of the Euler method for ordinary differential equations to stochastic differential equations named after Leonhard Euler and Gisiro Maruyama
Euler–Maruyama_method
Formula for 3D vector rotation
different parametrization. The rotation is described by four Euler parameters due to Leonhard Euler. The Rodrigues' rotation formula (named after Olinde Rodrigues)
Euler–Rodrigues_formula
Characterization of even perfect numbers
prime number. The theorem is named after mathematicians Euclid and Leonhard Euler, who respectively proved the "if" and "only if" aspects of the theorem
Euclid–Euler_theorem
Infinite products of functions indexed by primes
sum of all positive integers raised to a certain power as proven by Leonhard Euler. This series and its continuation to the entire complex plane would
Euler_product
Diagram of harmonic relations in music
conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739. Various visual representations of the Tonnetz can be used to
Tonnetz
Mathematical function
\phi (q)=\prod _{k=1}^{\infty }(1-q^{k}),\quad |q|<1.} Named after Leonhard Euler, it is a model example of a q-series and provides the prototypical example
Euler_function
of Leonhard Euler in four series collectively called Opera Omnia (Collected Works in Latin). The project represented a colossal challenge, as Euler is
Euler Committee of the Swiss Academy of Sciences
Euler_Committee_of_the_Swiss_Academy_of_Sciences
Number, approximately 3.14
π" (PDF). How Euler Did It. Reprinted in How Euler Did Even More. Mathematical Association of America. 2014. pp. 109–118. Euler, Leonhard (1755). "§ 2
Pi
American group dedicated to the life and work of Leonhard Euler
The Euler Society is an American group that is dedicated to the examination of the life and work of Leonhard Euler. Its first meeting was August 2002,
Euler_Society
Class of partial differential equations
In mathematical physics and differential geometry, the Euler–Arnold equations are a class of partial differential equations (PDEs) that describe the geodesic
Euler–Arnold_equation
Field of knowledge
in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler. The field came to full fruition with the contributions of Adrien-Marie
Mathematics
Enlightenment such as the mathematicians of the Bernoulli family and Leonhard Euler of Basel. The Old Swiss Confederacy between phases of expansion consisted
Early_modern_Switzerland
Mathematical concept
Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of
Euler_system
Swiss mathematician (1885–1970)
history of mathematics and was the chief editor for the Euler Commission's edition of Leonhard Euler's Opera Omnia and the editor of the works of Johann Heinrich
Andreas_Speiser
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
On distance between centers of a triangle
circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who published it in 1765. However, the same result was published earlier
Euler's_theorem_in_geometry
Square root of a non-positive real number
or useless, the concept gained wide acceptance following the work of Leonhard Euler in the 18th century, and Augustin-Louis Cauchy and Carl Friedrich Gauss
Imaginary_number
Movement with a fixed point is rotation
theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. The axis of rotation is known as an Euler axis, typically represented
Euler's_rotation_theorem
Square array with symbols that each occur once per row and column
square is The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols
Latin_square
Book by Leonhard Euler
Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis. Written in Latin
Introductio in analysin infinitorum
Introductio_in_analysin_infinitorum
Every graph has evenly many odd vertices
twice the number of edges in the graph. Both results were proven by Leonhard Euler (1736) in his famous paper on the Seven Bridges of Königsberg that began
Handshaking_lemma
Integrable rigid bodies in classical mechanics
The Hamiltonian is a function on this phase space. The Euler top, named after Leonhard Euler, is an untorqued top (for example, a top in free fall),
Lagrange, Euler, and Kovalevskaya tops
Lagrange,_Euler,_and_Kovalevskaya_tops
Constant equal to twice pi
whole. Leonhard Euler initially used the single letter π to denote the constant 6.28... in his 1727 Essay Explaining the Properties of Air. Euler would
Tau_(mathematics)
Mathematical identity
expansion Gauss's continued fraction List of topics named after Leonhard Euler Leonhard Euler (1748), "18", Introductio in analysin infinitorum, vol. I H
Euler's continued fraction formula
Euler's_continued_fraction_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
Perfect_number
German mathematician (1733–1813)
physics at the University of Utrecht. He was a significant student of Leonhard Euler. He was known for his inclination towards the British school of philosophy
Johann_Friedrich_Hennert
Chinese car marque
stands for "open, reliable and alternative", while also paying homage to Leonhard Euler, a notable Swiss mathematician whose surname is phonetically translated
Ora_(marque)
Relation between the sides of a convex quadrilateral and its diagonals
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex
Euler's_quadrilateral_theorem
Product of sums of four squares expressed as a sum of four squares
sixteen-square identity Latin square List of topics named after Leonhard Euler Leonhard Euler: Life, Work and Legacy, R.E. Bradley and C.E. Sandifer (eds)
Euler's_four-square_identity
Index of articles associated with the same name
( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} Leonhard Euler List of topics named after Leonhard Euler Jeffrey, Alan; Dai, Hui-Hui (2008). Handbook of
Euler_integral
Mathematical work by Leonhard Euler
of differential calculus) is a mathematical work written in 1748 by Leonhard Euler and published in 1755. It lays the groundwork for the differential calculus
Institutiones calculi differentialis
Institutiones_calculi_differentialis
Surname list
Euler is a German surname. Notable people with the surname include: Leonhard Euler (1707–1783), Swiss mathematician and physicist Carl Euler (1834–1901)
Euler_(surname)
Problem in physics and astronomy
fields of prolate and oblate spheroids. This problem is named after Leonhard Euler, who discussed it in memoirs published in 1760. Important extensions
Euler's_three-body_problem
17th-century conjecture proved by Andrew Wiles in 1994
exponents p = 3, 5, 7. In 1770, Leonhard Euler gave a proof of p = 3, but his proof contained a major gap. However, since Euler himself had proved the lemma
Fermat's_Last_Theorem
Swiss mathematician (1667–1748)
contributions to infinitesimal calculus and for educating the young Leonhard Euler. Johann was born in Basel, the son of Nicolaus Bernoulli, an apothecary
Johann_Bernoulli
Finnish-Swedish mathematician and astronomer (1740–1784)
66 papers in 16 years of his work there. A statement attributed to Leonhard Euler expresses high approval of Lexell's works: "Besides Lexell, such a paper
Anders_Johan_Lexell
Curved triangle with constant width
windows, by Leonardo da Vinci, who used it for a map projection, and by Leonhard Euler in his study of constant-width shapes. Other applications of the Reuleaux
Reuleaux_triangle
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