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Articles 31 - 60 of 769
Full-Text Articles in Physical Sciences and Mathematics
Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou
Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou
Euleriana
Review of The History of Mathematics: A Source-Based Approach (Vol. 2), Part I, by June Barrow-Green, Jeremy Gray, and Robin Wilson. MAA Press, 2022, 330 + xiv pages.
Variety And Variation, Christopher Goff, Erik R. Tou
Variety And Variation, Christopher Goff, Erik R. Tou
Euleriana
Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euleriana
A spotlight on the Euler Archive focusing on Euler and the Basel Problem.
Leonhard Euler’S Correspondence Schedule, Dominic Klyve
Leonhard Euler’S Correspondence Schedule, Dominic Klyve
Euleriana
In addition to his large number of published articles and books, Leonhard Euler engaged in a prolific correspondence with scientists, mathematicians, and administrators throughout his career. By compiling the dates of all of his known letters, as described in the Opera Omnia, we can get some understanding of Euler’s weekly schedule. We report here for the first time Euler’s preference, particularly during his Berlin Period, of writing letters on Tuesdays and Saturdays.
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker
Euleriana
This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …
The Solution Of A Problem Of Searching For Three Numbers, Of Which The Sum, Product, And The Sum Of Their Products Taken Two At A Time, Are Square Numbers, Mark R. Snavely, Philip Woodruff
The Solution Of A Problem Of Searching For Three Numbers, Of Which The Sum, Product, And The Sum Of Their Products Taken Two At A Time, Are Square Numbers, Mark R. Snavely, Philip Woodruff
Euleriana
This paper first appeared in Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 64-73 and is reprinted in Opera Omnia: Series 1, Volume 2, pp.519-530. Its Eneström number is E270. Euler improves his results significantly in "On Three Square Numbers, of Which the Sum and the Sum of Products Two Apiece will be a Square" (E523).
On A New Class Of Oscillations, Sylvio R. Bistafa
On A New Class Of Oscillations, Sylvio R. Bistafa
Euleriana
In this publication, Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an object subjected to two acting forces, one proportional to the distance travelled, the other one varying sinusoidally with time.
On A New Class Of Oscillations, Sylvio R. Bistafa
On A New Class Of Oscillations, Sylvio R. Bistafa
Euleriana
This publication was motivated by Krafft’s accidental observation of a suspended clock setting itself in constant motion as a pendulum. His analysis of the phenomenon led him to conclude that the vibration of the clock was solely due to imbalances in the clock's balance wheel. Next, he conceives a 'little machine' as he called it, in which a straight bar loaded by small weights at its extremities is free to oscillate about the center of gravity of a regular suspended clock. He then investigates different oscillating conditions, by calculating moments with different weights and lengths of the bar arms, to …
Review Of Change And Variations, Robert E. Bradley
Review Of Change And Variations, Robert E. Bradley
Euleriana
Review of Change and Variations: A History of Differential Equations to 1900, by Jeremy Gray, Springer Undergraduate Mathematics Series, 2021, 419 + xxii pages.
Conversations On Change, Christopher Goff, Erik Tou
Conversations On Change, Christopher Goff, Erik Tou
Euleriana
Welcome to Volume 2 of Euleriana! One of the pleasures of studying the his- tory of mathematics is reading how historical figures conversed with each other on topics of their era. In this volume, those conversations focus on differential equations—a subject which occupied Euler’s attention for much of his 56-year career. Throughout, we will see how he corresponded with many scholars of the day as he developed and refined his mathematical ideas.
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.
Larval Food Limitation In A Speyeria Butterfly (Nymphalidae): How Many Butterflies Can Be Supported?, Ryan I. Hill, Cassidi E. Rush, John Mayberry
Larval Food Limitation In A Speyeria Butterfly (Nymphalidae): How Many Butterflies Can Be Supported?, Ryan I. Hill, Cassidi E. Rush, John Mayberry
College of the Pacific Faculty Articles
For herbivorous insects the importance of larval food plants is obvious, yet the role of host abundance and density in conservation are relatively understudied. Populations of Speyeria butterflies across North America have declined and Speyeria adiaste is an imperiled species endemic to the southern California Coast Ranges. In this paper, we study the link between the food plant Viola purpurea quercetorum and abundance of its herbivore Speyeria adiaste clemencei to better understand the butterfly’s decline and aid in restoration of this and other Speyeria species. To assess the degree to which the larval food plant limits adult abundance of S. …