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Leonhard Euler

Index Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory. [1]

247 relations: Academician, Aeneid, Alexander Nevsky Lavra, Algebra, American Academy of Arts and Sciences, American Mathematical Monthly, Analytic number theory, Anders Johan Lexell, Anhalt-Dessau, Apologetics, Asteroid, Astronomer, Astronomy, Atheism, Augustin-Louis Cauchy, Augustus De Morgan, Basel, Basel problem, Berlin, Bernoulli family, Bernoulli number, Biblical inerrancy, Biblical inspiration, Buckling, Calculus, Calculus of variations, Calendar of saints (Lutheran), Calvinism, Carl Friedrich Gauss, Cartography, Cataract, Catherine I of Russia, Catherine the Great, Christiaan Huygens, Christian Goldbach, Christian Wolff (philosopher), Classical mechanics, Complex analysis, Complex number, Continuum mechanics, Convex polytope, Coprime integers, Corpuscular theory of light, Curve, Cyclops, Daniel Bernoulli, De Moivre's formula, Dekabristov Island, Denis Diderot, Density, ..., Diagram, Differential calculus, Differential equation, Disjoint sets, Divergence of the sum of the reciprocals of the primes, Dover Publications, E (mathematical constant), Elastic modulus, Element (mathematics), Elements of Algebra, Elizabeth of Russia, Engineer, Euclid, Euclid's theorem, Euclid–Euler theorem, Euclidean vector, Euler characteristic, Euler Committee of the Swiss Academy of Sciences, Euler diagram, Euler equations (fluid dynamics), Euler method, Euler number, Euler's formula, Euler's identity, Euler's theorem, Euler's totient function, Euler–Bernoulli beam theory, Euler–Lagrange equation, Euler–Maclaurin formula, Euler–Mascheroni constant, Eulerian path, Existence of God, Exponential function, Fermat's Last Theorem (book), Fermat's little theorem, Fermat's theorem on sums of two squares, Fluid dynamics, Force, Fourier series, Frederick the Great, French Academy of Sciences, Friederike Charlotte of Brandenburg-Schwedt, Function (mathematics), Gamma, Gamma function, Generality of algebra, Generalized continued fraction, Generalized hypergeometric function, Genus (mathematics), Geometry, Georg Gsell, German Standard German, Gottfried Wilhelm Leibniz, Graph theory, Greek language, Harmonic series (mathematics), Hebrew language, History of longitude, Hyperbolic function, Imaginary unit, Infinitesimal, Institutiones calculi differentialis, Institutionum calculi integralis, Internal energy, Intersection (set theory), Intracerebral hemorrhage, Introductio in analysin infinitorum, Inverse trigonometric functions, Inviscid flow, Irrational number, Isaac Newton, Ivan Saltykov, Jakob Emanuel Handmann, Johann Bernoulli, Johann Euler, Johann Friedrich Hennert, John Wiley & Sons, Joseph-Louis Lagrange, Königsberg, Kingdom of Prussia, Lagrange's four-square theorem, Largest known prime number, Lattice (music), Letters to a German Princess, Light, Linda Hall Library, List of things named after Leonhard Euler, Logarithm, Logic, Lunar theory, Lutheranism, Marquis de Condorcet, Martin Knutzen, Mast (sailing), Master of Philosophy, Mathematical analysis, Mathematical notation, Mathematician, Mathematics Magazine, Mechanica, Mechanics, Mersenne prime, Method of Fluxions, Monadology, Music theory, Natural logarithm, Neva River, New Math, Newton's identities, Nicolas Fuss, Nicolaus II Bernoulli, Non sequitur (literary device), Number theory, Numerical analysis, Opticks, Optics, Orbit, Oxford English Dictionary, Parallax, Perfect number, Peter II of Russia, Peter the Great, Physicist, Physics, Pi, Pi (letter), Pierre Bouguer, Pierre de Fermat, Pierre-Simon Laplace, Planar graph, Power series, Pregolya River, Pressure, Prime number, Prime number theorem, Prime Obsession, Princeton University Press, Proof of the Euler product formula for the Riemann zeta function, Prussian Academy of Sciences, Q-Pochhammer symbol, Quadratic reciprocity, Quartic function, Quarto, Rational number, Real number, René Descartes, Richard Aldington, Richard Feynman, Riehen, Riemann zeta function, Rigour, Royal Swedish Academy of Sciences, Russian Academy of Sciences, Russian Empire, Russian Navy, Saint Petersburg, Sanssouci, Second moment of area, Set (mathematics), Set theory, Seven Bridges of Königsberg, Seven Years' War, Sigma, Simon Antoine Jean L'Huilier, Smolensky Lutheran Cemetery, Speed of sound, Stepan Rumovsky, Strabismus, Subset, Swiss Academies of Arts and Sciences, Swiss franc, Swiss Standard German, Syllogism, Tensor product, The American Heritage Dictionary of the English Language, The Mathematical Intelligencer, Tonnetz, Topology, Transcendental function, Trigonometric functions, Trigonometry, University of Basel, University of St Andrews, Uranus, Velocity, Venn diagram, Virgil, Visual perception, Voltaire, Volume, Wave–particle duality, Webster's Dictionary, Welsh people, William Jones (mathematician), Zero element, 2,147,483,647, 2002 Euler. Expand index (197 more) »


An academician is a full member of an artistic, literary, or scientific academy.

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The Aeneid (Aeneis) is a Latin epic poem, written by Virgil between 29 and 19 BC, that tells the legendary story of Aeneas, a Trojan who travelled to Italy, where he became the ancestor of the Romans.

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Alexander Nevsky Lavra

Saint Alexander Nevsky Lavra or Saint Alexander Nevsky Monastery was founded by Peter I of Russia in 1710 at the eastern end of the Nevsky Prospekt in Saint Petersburg supposing that that was the site of the Neva Battle in 1240 when Alexander Nevsky, a prince, defeated the Swedes; however, the battle actually took place about away from that site.

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Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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American Academy of Arts and Sciences

The American Academy of Arts and Sciences is one of the oldest learned societies in the United States of America.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.

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Anders Johan Lexell

Anders Johan Lexell (24 December 1740 &ndash) was a Finnish-Swedish astronomer, mathematician, and physicist who spent most of his life in Imperial Russia, where he was known as Andrei Ivanovich Leksel (Андрей Иванович Лексель).

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Anhalt-Dessau was a principality of the Holy Roman Empire and later a duchy of the German Confederation.

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Apologetics (from Greek ἀπολογία, "speaking in defense") is the religious discipline of defending religious doctrines through systematic argumentation and discourse.

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Asteroids are minor planets, especially those of the inner Solar System.

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An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth.

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Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

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Atheism is, in the broadest sense, the absence of belief in the existence of deities.

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Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

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Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.

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Basel (also Basle; Basel; Bâle; Basilea) is a city in northwestern Switzerland on the river Rhine.

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Basel problem

The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1734 and read on 5 December 1735 in ''The Saint Petersburg Academy of Sciences''.

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Berlin is the capital and the largest city of Germany, as well as one of its 16 constituent states.

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Bernoulli family

The Bernoulli family of Basel is a patrician family, notable for having produced eight mathematically gifted academics who, between them, contributed to the foundations of applied mathematics and physics during the early modern period.

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Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.

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Biblical inerrancy

Biblical inerrancy, as formulated in the "Chicago Statement on Biblical Inerrancy", is the doctrine that the Protestant Bible "is without error or fault in all its teaching"; or, at least, that "Scripture in the original manuscripts does not affirm anything that is contrary to fact".

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Biblical inspiration

Biblical inspiration is the doctrine in Christian theology that the authors and editors of the Bible were led or influenced by God with the result that their writings may be designated in some sense the word of God.

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In science, buckling is a mathematical instability that leads to a failure mode.

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Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Calculus of variations

Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

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Calendar of saints (Lutheran)

The Lutheran Calendar of Saints is a listing which specifies the primary annual festivals and events that are celebrated liturgically by some Lutheran Churches in the United States.

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Calvinism (also called the Reformed tradition, Reformed Christianity, Reformed Protestantism, or the Reformed faith) is a major branch of Protestantism that follows the theological tradition and forms of Christian practice of John Calvin and other Reformation-era theologians.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

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Cartography (from Greek χάρτης chartēs, "papyrus, sheet of paper, map"; and γράφειν graphein, "write") is the study and practice of making maps.

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A cataract is a clouding of the lens in the eye which leads to a decrease in vision.

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Catherine I of Russia

Catherine I (Yekaterina I Alekseyevna, born, later known as Marta Samuilovna Skavronskaya; –) was the second wife of Peter the Great and Empress of Russia from 1725 until her death.

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Catherine the Great

Catherine II (Russian: Екатерина Алексеевна Yekaterina Alekseyevna; –), also known as Catherine the Great (Екатери́на Вели́кая, Yekaterina Velikaya), born Princess Sophie of Anhalt-Zerbst, was Empress of Russia from 1762 until 1796, the country's longest-ruling female leader.

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Christiaan Huygens

Christiaan Huygens (Hugenius; 14 April 1629 – 8 July 1695) was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution.

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Christian Goldbach

Christian Goldbach (March 18, 1690 – November 20, 1764) was a German mathematician who also studied law.

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Christian Wolff (philosopher)

Christian Wolff (less correctly Wolf,; also known as Wolfius; ennobled as Christian Freiherr von Wolff; 24 January 1679 – 9 April 1754) was a German philosopher.

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Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.

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Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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Corpuscular theory of light

In optics, the corpuscular theory of light, arguably set forward by Descartes (1637) states that light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity and possess impetus.

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In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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A cyclops (Κύκλωψ, Kyklōps; plural cyclopes; Κύκλωπες, Kyklōpes), in Greek mythology and later Roman mythology, is a member of a primordial race of giants, each with a single eye in the center of his forehead.

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Daniel Bernoulli

Daniel Bernoulli FRS (8 February 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family.

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De Moivre's formula

In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) and integer it holds that where is the imaginary unit.

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Dekabristov Island

Dekabristov Island (остров Декабристов), or 'Decembrists' Island, known before 1926 as Goloday Island (остров Голодай - possibly a corruption of a British merchant name Halliday) is an island in Vasileostrovsky District of Saint Petersburg, Russia, to the north of Vasilyevsky Island, separated from it by Smolenka River.

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Denis Diderot

Denis Diderot (5 October 171331 July 1784) was a French philosopher, art critic, and writer, best known for serving as co-founder, chief editor, and contributor to the Encyclopédie along with Jean le Rond d'Alembert.

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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.

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A diagram is a symbolic representation of information according to some visualization technique.

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Differential calculus

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Disjoint sets

In mathematics, two sets are said to be disjoint sets if they have no element in common.

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Divergence of the sum of the reciprocals of the primes

The sum of the reciprocals of all prime numbers diverges; that is: This was proved by Leonhard Euler in 1737, and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers.

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Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

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E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

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Elastic modulus

An elastic modulus (also known as modulus of elasticity) is a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it.

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Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

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Elements of Algebra

Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1770 in German.

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Elizabeth of Russia

Elizabeth Petrovna (Елизаве́та (Елисаве́та) Петро́вна) (–), also known as Yelisaveta or Elizaveta, was the Empress of Russia from 1741 until her death.

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Engineers, as practitioners of engineering, are people who invent, design, analyze, build, and test machines, systems, structures and materials to fulfill objectives and requirements while considering the limitations imposed by practicality, regulation, safety, and cost.

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Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclid's theorem

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.

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Euclid–Euler theorem

The Euclid–Euler theorem is a theorem in mathematics that relates perfect numbers to Mersenne primes.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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Euler Committee of the Swiss Academy of Sciences

The Euler Committee of the Swiss Academy of Sciences (also known as the Euler Committee or the Euler Commission) was founded in July 1907 with the objective of publishing the entire scientific production of Leonhard Euler in four series collectively called Opera Omnia (Collected Works in Latin).

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Euler diagram

Euler diagram is a diagrammatic means of representing sets and their relationships.

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Euler equations (fluid dynamics)

In fluid dynamics, the Euler equations are a set of quasilinear hyperbolic equations governing adiabatic and inviscid flow.

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Euler method

In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

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Euler number

In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.

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Euler's formula

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

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Euler's identity

In mathematics, Euler's identity (also known as Euler's equation) is the equality where Euler's identity is named after the Swiss mathematician Leonhard Euler.

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Euler's theorem

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, then where \varphi(n) is Euler's totient function.

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Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.

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Euler–Bernoulli beam theory

Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory)Timoshenko, S., (1953), History of strength of materials, McGraw-Hill New York is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams.

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Euler–Lagrange equation

In the calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation (although the latter name is ambiguous—see disambiguation page), is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary.

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Euler–Maclaurin formula

In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums.

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Euler–Mascheroni constant

The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.

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Eulerian path

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph which visits every edge exactly once.

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Existence of God

The existence of God is a subject of debate in the philosophy of religion and popular culture.

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Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

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Fermat's Last Theorem (book)

Fermat's Last Theorem is a popular science book (1997) by Simon Singh.

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Fermat's little theorem

Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.

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Fermat's theorem on sums of two squares

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p.

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Fluid dynamics

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.

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In physics, a force is any interaction that, when unopposed, will change the motion of an object.

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Fourier series

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.

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Frederick the Great

Frederick II (Friedrich; 24 January 171217 August 1786) was King of Prussia from 1740 until 1786, the longest reign of any Hohenzollern king.

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French Academy of Sciences

The French Academy of Sciences (French: Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research.

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Friederike Charlotte of Brandenburg-Schwedt

Friederike Charlotte Leopoldine Louise of Brandenburg-Schwedt (also often referred to as the Princess of Prussia; 18 August 1745 in Schwedt – 23 January 1808 in Altona) was a German aristocrat who lived as a secular canoness and ruled as the last Princess-abbess of Herford Abbey.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Gamma (uppercase, lowercase; gámma) is the third letter of the Greek alphabet.

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Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

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Generality of algebra

In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange,.

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Generalized continued fraction

In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.

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Generalized hypergeometric function

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.

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Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

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Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Georg Gsell

Georg Gsell (Георг Гзель; 28 January 1673 – 22 November 1740) was a Swiss Baroque painter, art consultant and art dealer.

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German Standard German

German Standard German, Standard German of Germany or High German of Germany is the variety of Standard German that is written and spoken in Germany.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Greek language

Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.

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Harmonic series (mathematics)

In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.

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Hebrew language

No description.

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History of longitude

The history of longitude is a record of the effort, by astronomers, cartographers and navigators over several centuries, to discover a means of determining longitude.

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Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

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In mathematics, infinitesimals are things so small that there is no way to measure them.

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Institutiones calculi differentialis

Institutiones calculi differentialis (Foundations of differential calculus) is a mathematical work written in 1748 by Leonhard Euler and published in 1755 that lays the groundwork for the differential calculus.

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Institutionum calculi integralis

Institutionum calculi integralis is a three-volume textbook written by Leonhard Euler and published in 1768.

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Internal energy

In thermodynamics, the internal energy of a system is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields.

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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Intracerebral hemorrhage

Intracerebral hemorrhage (ICH), also known as cerebral bleed, is a type of intracranial bleed that occurs within the brain tissue or ventricles.

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Introductio in analysin infinitorum

Introductio in analysin infinitorum (Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis.

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Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).

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Inviscid flow

Inviscid flow is the flow of an inviscid fluid, in which the viscosity of the fluid is equal to zero.

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Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Ivan Saltykov

Count Ivan Petrovich Saltykov (Иван Петрович Салтыков; (28 June 1730 – 14 November 1805) was a Russian Field Marshal, the Governor-General of Moscow from 1797 to 1804, and owner of the grand estate of Marfino.

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Jakob Emanuel Handmann

Portrait of Jakob Emanuel Handmann (1770). Jakob Emanuel Handmann (16 August 1718 in Basel – 3 November 1781 in Bern) was a Swiss painter specialised in portrait painting.

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Johann Bernoulli

Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.

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Johann Euler

Johann Albrecht Euler (27 November 1734 – 17 September 1800) was a Swiss-Russian astronomer and mathematician.

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Johann Friedrich Hennert

Johann Friedrich Hennert (19 October 1733 – 30 March 1813) was German-born and lectured in mathematics and physics at the University of Utrecht.

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John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Königsberg is the name for a former German city that is now Kaliningrad, Russia.

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Kingdom of Prussia

The Kingdom of Prussia (Königreich Preußen) was a German kingdom that constituted the state of Prussia between 1701 and 1918.

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Lagrange's four-square theorem

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares.

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Largest known prime number

The largest known prime number is 277,232,917 − 1, a number with 23,249,425 digits.

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Lattice (music)

In musical tuning, a lattice "is a way of modeling the tuning relationships of a just intonation system.

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Letters to a German Princess

Letters to a German Princess, On Different Subjects in Physics and Philosophy (French: Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie) were a series of 234 letters written by the mathematician Leonhard Euler between 1760 and 1762 addressed to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise.

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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum.

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Linda Hall Library

The Linda Hall Library is a privately endowed American library of science, engineering and technology located in Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest independently funded public library of science, engineering and technology in North America" and "among the largest science libraries in the world.".

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List of things named after Leonhard Euler

Leonhard Euler (1707–1783)In mathematics and physics, there are a large number of topics named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations.

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In mathematics, the logarithm is the inverse function to exponentiation.

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Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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Lunar theory

Lunar theory attempts to account for the motions of the Moon.

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Lutheranism is a major branch of Protestant Christianity which identifies with the theology of Martin Luther (1483–1546), a German friar, ecclesiastical reformer and theologian.

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Marquis de Condorcet

Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election.

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Martin Knutzen

Martin Knutzen (14 December 1713 – 29 January 1751) was a German philosopher, a follower of Christian Wolff and teacher of Immanuel Kant, to whom he introduced the physics of Isaac Newton.

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Mast (sailing)

The mast of a sailing vessel is a tall spar, or arrangement of spars, erected more or less vertically on the centre-line of a ship or boat.

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Master of Philosophy

The Master of Philosophy (abbr. M.Phil. or MPhil, sometimes Ph.M.; Latin Magister Philosophiae or Philosophiae Magister) is a postgraduate degree.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas.

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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

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Mechanica (Mechanica sive motus scientia analytice exposita; 1736) is a two-volume work published by mathematician Leonhard Euler, which describes analytically the mathematics governing movement.

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Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

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Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two.

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Method of Fluxions

Method of Fluxions is a book by Isaac Newton.

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The Monadology (La Monadologie, 1714) is one of Gottfried Leibniz’s best known works representing his later philosophy.

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Music theory

Music theory is the study of the practices and possibilities of music.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Neva River

The Neva (Нева́) is a river in northwestern Russia flowing from Lake Ladoga through the western part of Leningrad Oblast (historical region of Ingria) to the Neva Bay of the Gulf of Finland.

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New Math

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s.

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Newton's identities

In mathematics, Newton's identities, also known as the Newton–Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials.

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Nicolas Fuss

Nicolas Fuss (29 January 1755 – 4 January 1826), also known as Nikolai Fuss, was a Swiss mathematician, living most of his life in Imperial Russia.

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Nicolaus II Bernoulli

Nicolaus II Bernoulli, a.k.a. Niklaus Bernoulli, Nikolaus Bernoulli, (6 February 1695, Basel, Switzerland – 31 July 1726, St. Petersburg, Russia) was a Swiss mathematician as were his father Johann Bernoulli and one of his brothers, Daniel Bernoulli.

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Non sequitur (literary device)

A non-sequitur ("it does not follow") is a conversational and literary device, often used for comedic purposes.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light is a book by English natural philosopher Isaac Newton that was published in English in 1704.

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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet.

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Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

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Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.

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Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

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Peter II of Russia

Peter II Alexeyevich (Russian: Пётр II Алексеевич, Pyotr II Alekseyevich) (–) reigned as Emperor of Russia from 1727 until his death.

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Peter the Great

Peter the Great (ˈpʲɵtr vʲɪˈlʲikʲɪj), Peter I (ˈpʲɵtr ˈpʲɛrvɨj) or Peter Alexeyevich (p; –)Dates indicated by the letters "O.S." are in the Julian calendar with the start of year adjusted to 1 January.

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A physicist is a scientist who has specialized knowledge in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.

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Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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The number is a mathematical constant.

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Pi (letter)

Pi (uppercase Π, lowercase π; πι) is the sixteenth letter of the Greek alphabet, representing the sound.

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Pierre Bouguer

Pierre Bouguer (16 February 1698, Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

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Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

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Pregolya River

The Pregolya or Pregola (Прего́ля; Pregel; Prieglius; Pregoła) is a river in the Russian Kaliningrad Oblast exclave.

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Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Prime number theorem

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.

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Prime Obsession

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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Proof of the Euler product formula for the Riemann zeta function

Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis Variae observationes circa series infinitas (Various Observations about Infinite Series), published by St Petersburg Academy in 1737.

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Prussian Academy of Sciences

The Royal Prussian Academy of Sciences (Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Akademie der Künste, or "Arts Academy," to which "Berlin Academy" may also refer.

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Q-Pochhammer symbol

In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.

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Quadratic reciprocity

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

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Quartic function

In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

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Quarto (abbreviated Qto, 4to or 4°) is a book or pamphlet produced from full "blanksheets", each of which is printed with eight pages of text, four to a side, then folded twice to produce four leaves (that is, eight book pages).

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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Richard Aldington

Richard Aldington (8 July 1892 – 27 July 1962), born Edward Godfree Aldington, was an English writer and poet.

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Richard Feynman

Richard Phillips Feynman (May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics for which he proposed the parton model.

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Riehen (Swiss German: Rieche) is a municipality in the canton of Basel-Stadt in Switzerland.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

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Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.

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Royal Swedish Academy of Sciences

The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden.

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Russian Academy of Sciences

The Russian Academy of Sciences (RAS; Росси́йская акаде́мия нау́к (РАН) Rossíiskaya akadémiya naúk) consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such as libraries, publishing units, and hospitals.

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Russian Empire

The Russian Empire (Российская Империя) or Russia was an empire that existed across Eurasia and North America from 1721, following the end of the Great Northern War, until the Republic was proclaimed by the Provisional Government that took power after the February Revolution of 1917.

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Russian Navy

The Russian Navy (r, lit. Military-Maritime Fleet of the Russian Federation) is the naval arm of the Russian Armed Forces.

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Saint Petersburg

Saint Petersburg (p) is Russia's second-largest city after Moscow, with 5 million inhabitants in 2012, part of the Saint Petersburg agglomeration with a population of 6.2 million (2015).

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Sanssouci is the summer palace of Frederick the Great, King of Prussia, in Potsdam, near Berlin.

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Second moment of area

The 2nd moment of area, also known as moment of inertia of plane area, area moment of inertia, or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Seven Bridges of Königsberg

The Seven Bridges of Königsberg is a historically notable problem in mathematics.

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Seven Years' War

The Seven Years' War was a global conflict fought between 1756 and 1763.

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Sigma (upper-case Σ, lower-case σ, lower-case in word-final position ς; σίγμα) is the eighteenth letter of the Greek alphabet.

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Simon Antoine Jean L'Huilier

Simon Antoine Jean L'Huilier (or L'Huillier) (24 April 1750 in Geneva – 28 March 1840 in Geneva) was a Swiss mathematician of French Hugenot descent.

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Smolensky Lutheran Cemetery

The Smolenskoye Cemetery (in German Smolensker Friedhof) is a Lutheran cemetery on Dekabristov Island in Saint Petersburg, Russia.

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Speed of sound

The speed of sound is the distance travelled per unit time by a sound wave as it propagates through an elastic medium.

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Stepan Rumovsky

Stepan Yakovlevich Rumovsky (Степан Яковлевич Румовский;, Vladimir Governorate –, Saint Petersburg) was a Russian astronomer and mathematician, considered to be the first Russian astronomer of renown.

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Strabismus, also known as crossed eyes, is a condition in which the eyes do not properly align with each other when looking at an object.

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In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Swiss Academies of Arts and Sciences

The Swiss Academies of Arts and Sciences is a Swiss organization that supports and networks the sciences at a regional, national and international level.

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Swiss franc

The franc (sign: Fr. or SFr.; Franken, French and Romansh: franc, franco; code: CHF) is the currency and legal tender of Switzerland and Liechtenstein; it is also legal tender in the Italian exclave Campione d'Italia.

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Swiss Standard German

Swiss Standard German (Schweizer Standarddeutsch), or Swiss High German (Schweizer Hochdeutsch or Schweizerhochdeutsch), referred to by the Swiss as Schriftdeutsch, or Hochdeutsch, is the written form of one of four official languages in Switzerland, besides French, Italian and Romansh.

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A syllogism (συλλογισμός syllogismos, "conclusion, inference") is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

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Tensor product

In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.

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The American Heritage Dictionary of the English Language

The American Heritage Dictionary of the English Language (AHD) is an American dictionary of English published by Boston publisher Houghton Mifflin, the first edition of which appeared in 1969.

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The Mathematical Intelligencer

The Mathematical Intelligencer is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.

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In musical tuning and harmony, the Tonnetz (tone-network) is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739.

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In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Transcendental function

A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

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University of Basel

The University of Basel (German: Universität Basel) is located in Basel, Switzerland.

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University of St Andrews

The University of St Andrews (informally known as St Andrews University or simply St Andrews; abbreviated as St And, from the Latin Sancti Andreae, in post-nominals) is a British public research university in St Andrews, Fife, Scotland.

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Uranus is the seventh planet from the Sun.

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The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

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Venn diagram

A Venn diagram (also called primary diagram, set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets.

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Publius Vergilius Maro (traditional dates October 15, 70 BC – September 21, 19 BC), usually called Virgil or Vergil in English, was an ancient Roman poet of the Augustan period.

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Visual perception

Visual perception is the ability to interpret the surrounding environment using light in the visible spectrum reflected by the objects in the environment.

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François-Marie Arouet (21 November 1694 – 30 May 1778), known by his nom de plume Voltaire, was a French Enlightenment writer, historian and philosopher famous for his wit, his attacks on Christianity as a whole, especially the established Catholic Church, and his advocacy of freedom of religion, freedom of speech and separation of church and state.

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Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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Wave–particle duality

Wave–particle duality is the concept in quantum mechanics that every particle or quantic entity may be partly described in terms not only of particles, but also of waves.

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Webster's Dictionary

Webster's Dictionary is any of the dictionaries edited by Noah Webster in the early nineteenth century, and numerous related or unrelated dictionaries that have adopted the Webster's name.

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Welsh people

The Welsh (Cymry) are a nation and ethnic group native to, or otherwise associated with, Wales, Welsh culture, Welsh history, and the Welsh language.

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William Jones (mathematician)

William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his use of the symbol (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter.

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Zero element

In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures.

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The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1.

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2002 Euler

2002 Euler, provisional designation, is a stony asteroid from the inner regions of the asteroid belt, approximately 17 kilometers in diameter.

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[1] https://en.wikipedia.org/wiki/Leonhard_Euler

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