72 Facts About Euler

Leonhard Euler was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

Euler introduced much of modern mathematical terminology and notation, including the notion of a mathematical function.

Euler is known for his work in mechanics, fluid dynamics, optics, astronomy and music theory.

Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century.

Euler spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.

Related searches

Euler gave the current definition of the constant, the base of the natural logarithm, now known as Euler's number.

Euler became famous for, among many other accomplishments, solving the Basel problem, after proving that the sum of the infinite series of squared integer reciprocals equaled exactly, and for discovering that the sum of the numbers of vertices and faces minus edges of a polyhedron equals 2, a number now commonly known as the Euler characteristic.

Euler made substantial contributions to the study of elastic deformations of solid objects.

From a young age, Euler received schooling in mathematics from his father, who had taken courses from Jacob Bernoulli some years earlier at the University of Basel.

Around the age of eight, Euler was sent to live at his maternal grandmother's house and enrolled in the Latin school in Basel.

In 1723, Euler received a Master of Philosophy with a dissertation that compared the philosophies of Rene Descartes and Isaac Newton.

In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono with which he unsuccessfully attempted to obtain a position at the University of Basel.

Euler was promoted from his junior post in the medical department of the academy to a position in the mathematics department.

Euler lodged with Daniel Bernoulli with whom he worked in close collaboration.

Euler mastered Russian, settled into life in Saint Petersburg and took on an additional job as a medic in the Russian Navy.

Euler swiftly rose through the ranks in the academy and was made a professor of physics in 1731.

Euler left the Russian Navy, refusing a promotion to lieutenant.

Euler succeeded him as the head of the mathematics department.

Euler lived for 25 years in Berlin, where he wrote several hundred articles.

Euler became the tutor for Friederike Charlotte of Brandenburg-Schwedt, the Princess of Anhalt-Dessau and Frederick's niece.

Euler wrote over 200 letters to her in the early 1760s, which were later compiled into a volume entitled Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess.

Euler was a simple, devoutly religious man who never questioned the existing social order or conventional beliefs.

Euler was, in many ways, the polar opposite of Voltaire, who enjoyed a high place of prestige at Frederick's court.

Euler was not a skilled debater and often made it a point to argue subjects that he knew little about, making him the frequent target of Voltaire's wit.

Euler assisted students from the St Petersburg academy and at times accommodated Russian students in his house in Berlin.

Related searches

Euler decided to leave Berlin in 1766 and return to Russia.

Euler was even involved in the design of the water fountains at Sanssouci, the King's summer palace.

Political situation in Russia stabilized after Catherine the Great's accession to the throne, so in 1766 Euler accepted an invitation to return to the St Petersburg Academy.

Euler's conditions were quite exorbitant—a 3000 ruble annual salary, a pension for his wife, and the promise of high-ranking appointments for his sons.

Euler blamed the cartography he performed for the St Petersburg Academy for his condition, but the cause of his blindness remains the subject of speculation.

Jacob von Staehlin wrote a short obituary for the Russian Academy of Sciences and Russian mathematician Nicolas Fuss, one of Euler's disciples, wrote a more detailed eulogy, which he delivered at a memorial meeting.

Euler was buried next to Katharina at the Smolensk Lutheran Cemetery on Vasilievsky Island.

Euler worked in almost all areas of mathematics, including geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory, and other areas of physics.

Euler is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes.

Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks.

Development of infinitesimal calculus was at the forefront of 18th-century mathematical research, and the Bernoullis—family friends of Euler—were responsible for much of the early progress in the field.

Euler introduced the use of the exponential function and logarithms in analytic proofs.

Euler discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms.

Euler defined the exponential function for complex numbers and discovered its relation to the trigonometric functions.

Euler elaborated the theory of higher transcendental functions by introducing the gamma function and introduced a new method for solving quartic equations.

Euler found a way to calculate integrals with complex limits, foreshadowing the development of modern complex analysis.

Euler invented the calculus of variations and formulated the Euler–Lagrange equation for reducing optimization problems in this area to the solution of differential equations.

Euler pioneered the use of analytic methods to solve number theory problems.

In breaking ground for this new field, Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions, and the analytic theory of continued fractions.

Euler developed some of Fermat's ideas and disproved some of his conjectures, such as his conjecture that all numbers of the form are prime.

Related searches

Euler linked the nature of prime distribution with ideas in analysis.

Euler proved that the sum of the reciprocals of the primes diverges.

Euler invented the totient function f, the number of positive integers less than or equal to the integer n that are coprime to n Using properties of this function, he generalized Fermat's little theorem to what is known as Euler's theorem.

Euler contributed significantly to the theory of perfect numbers, which had fascinated mathematicians since Euclid.

Euler proved that the relationship shown between even perfect numbers and Mersenne primes was one-to-one, a result otherwise known as the Euclid–Euler theorem.

Euler contributed major developments to the theory of partitions of an integer.

In 1735, Euler presented a solution to the problem known as the Seven Bridges of Konigsberg.

Euler discovered the formula relating the number of vertices, edges, and faces of a convex polyhedron, and hence of a planar graph.

Euler integrated Leibniz's differential calculus with Newton's Method of Fluxions, and developed tools that made it easier to apply calculus to physical problems.

Euler made great strides in improving the numerical approximation of integrals, inventing what are now known as the Euler approximations.

Euler helped develop the Euler–Bernoulli beam equation, which became a cornerstone of engineering.

Euler's accomplishments include determining with great accuracy the orbits of comets and other celestial bodies, understanding the nature of comets, and calculating the parallax of the Sun.

Euler's calculations contributed to the development of accurate longitude tables.

Euler disagreed with Newton's corpuscular theory of light, which was the prevailing theory of the time.

In fluid dynamics, Euler was the first to predict the phenomenon of cavitation, in 1754, long before its first observation in the late 19th century, and the Euler number used in fluid flow calculations comes from his related work on the efficiency of turbines.

Euler is well known in structural engineering for his formula giving Euler's critical load, the critical buckling load of an ideal strut, which depends only on its length and flexural stiffness.

Euler is credited with using closed curves to illustrate syllogistic reasoning .

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

Euler diagrams consist of simple closed curves in the plane that depict sets.

Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s.

Related searches

Euler later envisaged the possibility of describing genres including the prime number 7.

Euler devised a specific graph, the Speculum musicum, to illustrate the diatonico-chromatic genre, and discussed paths in this graph for specific intervals, recalling his interest in the Seven Bridges of Konigsberg .

Euler further used the principle of the "exponent" to propose a derivation of the gradus suavitatis of intervals and chords from their prime factors – one must keep in mind that he considered just intonation, i e 1 and the prime numbers 3 and 5 only.

Euler opposed the concepts of Leibniz's monadism and the philosophy of Christian Wolff.

Euler insisted that knowledge is founded in part on the basis of precise quantitative laws, something that monadism and Wolffian science were unable to provide.

Euler was featured on both the sixth and seventh series of the Swiss 10-franc banknote and on numerous Swiss, German, and Russian postage stamps.

The Euler Archive was started at Dartmouth College before moving to the Mathematical Association of America and, most recently, to University of the Pacific in 2017.