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Full-Text Articles in Physical Sciences and Mathematics
Euler's De Serie Lambertina, Translated From Latin To English With Supplementary Notes, Sam Gallagher
Euler's De Serie Lambertina, Translated From Latin To English With Supplementary Notes, Sam Gallagher
Euleriana
Originally published in 1779, Euler's De Serie Lambertina provides one of the early examples of the Lambert W function, a special function used in the solution to certain transcendental equations. Following the work of Johann Heinrich Lambert in 1759, who discussed a series solution to the general polynomial in series, and then particularly the solution of the general trinomial, Euler describes a symmetric form of the trinomial and its series solution. Euler investigates the series' special cases and general properties, and its use in solving certain transcendental equations. He provides several proofs of the validity of the series expansion to …
Translation Of Euler's Paper E421, Alexander Aycock
Translation Of Euler's Paper E421, Alexander Aycock
Euleriana
This is paper is the result of Euler’s findings on the Eulerian integral of second kind, i.e. the Γ-function: It summarises results and formulas on and properties of the integral in the title that Euler had obtained up to this point in his career and offers more elegant proofs of those before-mentioned results, formulas and properties. The results include a derivation of the integral in the title from an algebraic integral, the reflection formula for the Γ-function and finally a formula equivalent to the Gaußian multiplication formula for the Γ-function, expressed by Euler using mere integrals of algebraic functions.
Euler And The Multiplication Formula For The Gamma Function, Alexander Aycock
Euler And The Multiplication Formula For The Gamma Function, Alexander Aycock
Euleriana
We show that an apparently overlooked result of Leonhard Euler (1707-1783) from [E421] is essentially equivalent to the general multiplication for- mula for the Γ-function that was proven by Carl Friedrich Gauss (1777-1855) in [Ga28].
On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa
On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa
Euleriana
This is an annotated translation from Latin of E327 -- De motu rectilineo trium corporum se mutuo attrahentium (“On the rectilinear motion of three bodies mutually attracting each other”). In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Here Euler finds that the parameter that controls the relative distances among the bodies is given by a quintic function.
Euler's Miracle, William Dunham
Euler's Miracle, William Dunham
Euleriana
This article features some genuine Eulerian magic. In 1748, Leonhard Euler considered a modification of the harmonic series in which negative signs were attached to various terms by a rule that was far from self-evident. With his accustomed flair, he determined its sum, and the result was utterly improbable. There are a few occasions in mathematics when the term “breathtaking” is not too strong. This is one of them.
Spotlight On The Euler Archive, Cynthia J. Huffman Ph.D.
Spotlight On The Euler Archive, Cynthia J. Huffman Ph.D.
Euleriana
A spotlight on the Euler Archive with a special emphasis on contributions by Dr. C. Edward Sandifer.
Ed Sandifer: An Eulerian Marathoner, Robert E. Bradley
Ed Sandifer: An Eulerian Marathoner, Robert E. Bradley
Euleriana
Ed Sandifer was the founding secretary of the Euler Society. He published a remarkable quantity of Euler scholarship at the time of Euler’s Tercentenary in 2007.
Review: A History Of Mathematics In The United States And Canada (Vol. 1), By David Zitarelli, Lawrence D'Antonio
Review: A History Of Mathematics In The United States And Canada (Vol. 1), By David Zitarelli, Lawrence D'Antonio
Euleriana
This is a review of the 2019 text by David ZItarelli, A History of Mathematics in the United States and Canada. Volume 1: 1492 - 1900
Sharing Contributions To Euler Scholarship, Erik R. Tou, Christopher Goff
Sharing Contributions To Euler Scholarship, Erik R. Tou, Christopher Goff
Euleriana
A summary of this issue's contents.
Euler In Wartime: Publishing In The Seven Years' War, Erik R. Tou
Euler In Wartime: Publishing In The Seven Years' War, Erik R. Tou
Euleriana
At the outbreak of the Seven Years' War in 1756, Leonhard Euler (1707-1783) was a successful and prolific scholar at the Berlin Academy of Sciences, well on his way to producing many significant contributions to 18th century science and mathematics. However, once the war began his opportunities were sharply curtailed. Most of the war did not go well for Prussia, and Euler's place in the midst of this conflict limited his ability to publish his work. With the Euler Archive available online, Gustaf Eneström's index may be analyzed more deeply to uncover the effects of the conflict on Euler's life …
Euler Archive Spotlight, Cynthia J. Huffman Ph.D.
Euler Archive Spotlight, Cynthia J. Huffman Ph.D.
Euleriana
A spotlight on the Euler Archive, including recent translations.
Euler’S Theories Of Musical Tuning With An English Translation Of Du Véritable Caractère De La Musique Moderne, Larry G. Blaine, Susan Ferré
Euler’S Theories Of Musical Tuning With An English Translation Of Du Véritable Caractère De La Musique Moderne, Larry G. Blaine, Susan Ferré
Euleriana
Du Véritable Caractère de la Musique Moderne (E315), a work almost unknown to musical scholars, is an extremely interesting document in the history of tuning systems. A tuning system is simply an arrangement of sound frequencies for use in music. A just tuning is an arrangement in which the ratios of these frequencies are all ratios of whole numbers- preferably small ones. Classically, these ratios involve only factors of 2, 3, and 5. In particular, a very fundamental chord in music of many genres, the so-called major triad, Has frequency ratios 4:5:6. Euler proposes introducing the prime 7, …
Principles For Determining The Motion Of Blood Through Arteries, Sylvio R. Bistafa
Principles For Determining The Motion Of Blood Through Arteries, Sylvio R. Bistafa
Euleriana
Translation of Principia pro motu sanguinis per arterias determinando (E855). This work of 1775 by L. Euler is considered to be the first mathematical treatment of circulatory physiology and hemodynamics.
Euler, Father Of Haemodynamics, Sylvio R. Bistafa
Euler, Father Of Haemodynamics, Sylvio R. Bistafa
Euleriana
This article is being published in conjunction with the translation and synopsis of E855. Principia pro motu sanguinis per arterias determinando of 1775 - view the translation and synopsis by clicking here.
A History And Translation Of Lagrange's "Sur Quelques Problèmes De L'Analyse De Diophante'', Christopher Goff, Michael Saclolo
A History And Translation Of Lagrange's "Sur Quelques Problèmes De L'Analyse De Diophante'', Christopher Goff, Michael Saclolo
Euleriana
Among Lagrange's many achievements in number theory is a solution to the problem posed and solved by Fermat of finding a right triangle whose legs sum to a perfect square and whose hypotenuse is also a square. This article chronicles various appearances of the problem, including multiple solutions by Euler, all of which inadequately address completeness and minimality of solutions. Finally, we summarize and translate Lagrange's paper in which he solves the problem completely, thus successfully proving the minimality of Fermat's original solution.
On The Surface Area Of Scalene Cones And Other Conical Bodies, Daniel J. Curtin
On The Surface Area Of Scalene Cones And Other Conical Bodies, Daniel J. Curtin
Euleriana
This paper first appeared in the Novi Commentarii academiae scientiarum Petropolitanae vol. 1, 1750, pp. 3-19 and is reprinted in the Opera Omnia: Series 1, Volume 27, pp. 181–199. Its Eneström number is E133. This translation and the Latin original are available from the Euler Archive.
The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin
The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin
Euleriana
In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon's in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz's solution, which he corrected, after extending Varignon's solution in the case of circular base. Euler then used Leibniz's approach to solve …
Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney
Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney
Euleriana
We give a brief history of the Euler Archive, an online database of the published works of Leonhard Euler (1707-1783). Furthermore, we describe the Archive's recent move to an academic repository, and the added functionality such a move allows.
A New Look At Euler And His Contemporaries, Christopher Goff, Erik Tou
A New Look At Euler And His Contemporaries, Christopher Goff, Erik Tou
Euleriana
Introducing Euleriana: Volume 1, Issue 1.