%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.05", %%% date = "26 September 2024", %%% time = "14:01:34 MDT", %%% filename = "euleriana.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "62990 1896 8169 80186", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Euleriana; Leonhard %%% Euler", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of the %%% open-access mathematics history journal, %%% Euleriana (CODEN none, ISSN 2693-9908), %%% published by the University of the Pacific %%% and the University of Washington Tacoma. %%% %%% Publication began with volume 1, number 1, %%% in 2021, and there are two issues per annual %%% volume. %%% %%% The journal has a Web site at %%% %%% https://scholarlycommons.pacific.edu/euleriana/ %%% %%% At version 1.05, the COMPLETE journal %%% coverage looked like this: %%% %%% 2021 ( 20) 2023 ( 15) %%% 2022 ( 17) 2024 ( 14) %%% %%% Article: 66 %%% %%% Total entries: 66 %%% %%% Data for this bibliography have been derived, %%% with manual corrections, from the journal Web %%% site. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\input bibnames.sty" # "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" # "\ifx \undefined \circled \def \circled #1{(#1)}\fi" # "\ifx \undefined \reg \def \reg {\circled{R}}\fi" # "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-EULERIANA = "Euleriana"} %%% ==================================================================== %%% Notes on BibTeX entry production in this file: %%% %%% (1) Article PDF files are paginated, but the page ranges are not %%% recorded in the journal Web site metadata. %%% %%% (2) DOI data are recorded in individual article Web pages, but not %%% in the journal Web site article metadata; they have been %%% manually added to this file from data lookups for guessed DOIs %%% at https://doi.org/, along with starting page ranges and issue %%% months. %%% %%% (3) Abstracts have been extracted automatically from article %%% metadata. %%% ==================================================================== %%% Bibliography entries: @Article{Goff:2021:NLE, author = "Christopher Goff and Erik Tou", title = "A New Look at {Euler} and his Contemporaries", journal = j-EULERIANA, volume = "1", number = "1", pages = "1--3", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1012", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/1", abstract = "Introducing Euleriana: Volume 1, Issue 1.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2021:CWH, author = "Erik R. Tou and Christopher Goff and Michele Gibney", title = "Collecting Works: A History of the {Euler Archive}", journal = j-EULERIANA, volume = "1", number = "1", pages = "4--9", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1010", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/2", abstract = "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.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Curtin:2021:SASa, author = "Daniel J. Curtin", title = "The Surface Area of a Scalene Cone as Solved by {Varignon}, {Leibniz}, and {Euler}", journal = j-EULERIANA, volume = "1", number = "1", pages = "10--41", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1006", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/3", abstract = "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 the general problem. This paper examines all three articles, including English translations.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Curtin:2021:SASb, author = "Daniel J. Curtin", title = "On the Surface Area of Scalene Cones and Other Conical Bodies", journal = j-EULERIANA, volume = "1", number = "1", pages = "42--61", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1013", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/4", abstract = "This paper first appeared in the Novi Commentarii academiae scientiarum Petropolitanae vol. 1, 1750, pp. 3--19 and is reprinted in the \booktitle{Opera Omnia}: Series 1, Volume 27, pp. 181--199. Its Enestr{\"o}m number is E133. This translation and the Latin original are available from the Euler Archive.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2021:HTL, author = "Christopher Goff and Michael Saclolo", title = "A History and Translation of {Lagrange}'s \booktitle{``Sur quelques probl{\`e}mes de l'analyse de Diophante''}", journal = j-EULERIANA, volume = "1", number = "1", pages = "62--87", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1002", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/5", abstract = "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.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2021:EFH, author = "Sylvio R. Bistafa", title = "{Euler}, Father of Haemodynamics", journal = j-EULERIANA, volume = "1", number = "1", pages = "88--92", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1007", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/6", abstract = "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.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2021:PDM, author = "Sylvio R. Bistafa", title = "Principles for Determining The Motion of Blood Through Arteries", journal = j-EULERIANA, volume = "1", number = "1", pages = "93--111", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1004", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/7", abstract = "Translation of \booktitle{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.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Blaine:2021:ETM, author = "Larry G. Blaine and Susan Ferr{\'e}", title = "{Euler}'s Theories of Musical Tuning With an {English} Translation of {{\booktitle{Du V{\'e}ritable Caract{\`e}re de la Musique Moderne}}}", journal = j-EULERIANA, volume = "1", number = "1", pages = "112--140", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1003", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/8", abstract = "Du V{\'e}ritable Caract{\`e}re 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, with a fundamental chord made up of ratios 4:5:6:7. Not only that, but he asserts that modern composers are already using such ratios, albeit in a disguised or subliminal form. These ideas have had little lasting influence- indeed, Euler himself seems to have abandoned them later, as is pointed out in the notes to this translation. Nevertheless they are striking as an example of a certain type of logic pushed to the extreme.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{PhD:2021:EAS, author = "Cynthia J. Huffman", title = "{Euler Archive} Spotlight", journal = j-EULERIANA, volume = "1", number = "1", pages = "141--143", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1008", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/9", abstract = "A spotlight on the Euler Archive, including recent translations.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2021:EWP, author = "Erik R. Tou", title = "{Euler} in Wartime: Publishing in the {Seven Years' War}", journal = j-EULERIANA, volume = "1", number = "1", pages = "144--156", month = feb, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1009", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/10", abstract = "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 Enestr{\"o}m's index may be analyzed more deeply to uncover the effects of the conflict on Euler's life and work. In particular, we will see how Euler relied on his ties to the St. Petersburg Academy to present his work to the world.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2021:SCE, author = "Erik R. Tou and Christopher Goff", title = "Sharing Contributions to {Euler} Scholarship", journal = j-EULERIANA, volume = "1", number = "2", pages = "157--158", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1023", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/1", abstract = "A summary of this issue's contents.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{DAntonio:2021:RHM, author = "Lawrence D'Antonio", title = "Review: {{\booktitle{A History of Mathematics in the United States and Canada}} (Vol. 1), by David Zitarelli}", journal = j-EULERIANA, volume = "1", number = "2", pages = "159--164", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1019", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/2", abstract = "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", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bradley:2021:ESE, author = "Robert E. Bradley", title = "{Ed Sandifer}: An {Eulerian} Marathoner", journal = j-EULERIANA, volume = "1", number = "2", pages = "165--167", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1022", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/3", abstract = "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.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", subject-dates = "Ed Sandifer (1951--)", } @Article{PhD:2021:SEA, author = "Cynthia J. Huffman", title = "Spotlight on the {Euler Archive}", journal = j-EULERIANA, volume = "1", number = "2", pages = "168--171", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1018", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/4", abstract = "A spotlight on the Euler Archive with a special emphasis on contributions by Dr. C. Edward Sandifer.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Dunham:2021:EM, author = "William Dunham", title = "{Euler}'s Miracle", journal = j-EULERIANA, volume = "1", number = "2", pages = "172--180", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1014", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/5", abstract = "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.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2021:ETB, author = "Sylvio R. Bistafa", title = "{Euler}'s three-body problem", journal = j-EULERIANA, volume = "1", number = "2", pages = "181--187", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1017", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/6", abstract = "In physics and astronomy, Euler's three-body problem is to solve for the motion of a body that is acted upon by the gravitational field of two other bodies. This problem is named after Leonhard Euler (1707--1783), who discussed it in memoirs published in the 1760s. In these publications, Euler found that the parameter that controls the relative distances among three collinear bodies is given by a quintic equation. Later on, in 1772, Lagrange dealt with the same problem, and demonstrated that for any three masses with circular orbits, there are two special constant-pattern solutions, one where the three bodies remain collinear, and the other where the bodies occupy the vertices of two equilateral triangles. Because of their importance, these five points became known as Lagrange points. The quintic equation found by Euler for the relative distances among the collinear bodies was also found later by Lagrange, and because of that, Euler has also been given credit for the discovery of the three collinear Lagrange points. A practical application of the collinear points for satellite location is also presented.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2021:RMT, author = "Sylvio R. Bistafa", title = "On the Rectilinear Motion of Three Bodies Mutually Attracting Each Other", journal = j-EULERIANA, volume = "1", number = "2", pages = "188--196", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1016", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/7", abstract = "This is an annotated translation from Latin of E327 -- \booktitle{De motu rectilineo trium corporum se mutuo attrahentium} (\booktitle{``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.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2021:EMF, author = "Alexander Aycock", title = "{Euler} and the multiplication formula for the Gamma Function", journal = j-EULERIANA, volume = "1", number = "2", pages = "197--204", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1000", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/8", abstract = "We show that an apparently overlooked result of Leonhard Euler (1707--1783) from [E421] is essentially equivalent to the general multiplication formula for the $ \Gamma $-function that was proven by Carl Friedrich Gauss (1777--1855) in [Ga28].", acknowledgement = ack-nhfb, articleno = "8", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2021:TEP, author = "Alexander Aycock", title = "Translation of {Euler}'s Paper {E421}", journal = j-EULERIANA, volume = "1", number = "2", pages = "205--251", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1001", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/9", abstract = "This is paper is the result of Euler's findings on the Eulerian integral of second kind, i.e. the $ \Gamma $-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 $ \Gamma $-function and finally a formula equivalent to the Gau{\ss}ian multiplication formula for the $ \Gamma $-function, expressed by Euler using mere integrals of algebraic functions.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Gallagher:2021:ESL, author = "Sam Gallagher", title = "{Euler}'s {{\booktitle{De Serie Lambertina}}}, Translated from {Latin} to {English} With Supplementary Notes", journal = j-EULERIANA, volume = "1", number = "2", pages = "252--272", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1015", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:26 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol1/iss2/10", abstract = "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 solve the trinomial, and in doing so he reveals several notable series expansions of functions such as the natural logarithm and the factorial.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2022:CC, author = "Christopher Goff and Erik Tou", title = "Conversations on Change", journal = j-EULERIANA, volume = "2", number = "1", pages = "1--2", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1035", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/1", abstract = "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.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bradley:2022:RCV, author = "Robert E. Bradley", title = "Review of {{\booktitle{Change and Variations}}}", journal = j-EULERIANA, volume = "2", number = "1", pages = "3--5", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1030", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/2", abstract = "Review of Change and Variations: A History of Differential Equations to 1900, by Jeremy Gray, Springer Undergraduate Mathematics Series, 2021, 419 + xxii pages.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2022:NCOa, author = "Sylvio R. Bistafa", title = "On a New Class of Oscillations", journal = j-EULERIANA, volume = "2", number = "1", pages = "6--10", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1033", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/4", abstract = "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 find conditions to attain oscillating excursions in a right angle, excursions with maximum amplitude, and showing that the vibrations of the whole clock are rendered more sensible, the shorter is the height of the suspension.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2022:NCOb, author = "Sylvio R. Bistafa", title = "On a New Class of Oscillations", journal = j-EULERIANA, volume = "2", number = "1", pages = "11--26", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1031", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/3", abstract = "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.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Snavely:2022:SPS, author = "Mark R. Snavely and Philip Woodruff", title = "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", journal = j-EULERIANA, volume = "2", number = "1", pages = "27--39", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1020", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/5", abstract = "This paper first appeared in Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 64--73 and is reprinted in \booktitle{Opera Omnia}: Series 1, Volume 2, pp. 519--530. Its Enestr{\"o}m number is E270. Euler improves his results significantly in \booktitle{``On Three Square Numbers, of Which the Sum and the Sum of Products Two Apiece will be a Square''} (E523).", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Barnett:2022:LMM, author = "Janet Heine Barnett and Dominic Klyve and Kenneth M. Monks and Adam E. Parker", title = "Learning Mathematics from the Master: A Collection of {Euler}-based Primary Source Projects for Today's Students, {Part I}", journal = j-EULERIANA, volume = "2", number = "1", pages = "40--50", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1027", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/6", abstract = "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 use.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Klyve:2022:LEC, author = "Dominic Klyve", title = "{Leonhard Euler}'s Correspondence Schedule", journal = j-EULERIANA, volume = "2", number = "1", pages = "51--55", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1029", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/7", abstract = "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 \booktitle{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.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{PhD:2022:EASa, author = "Cynthia Huffman", title = "{Euler Archive} Spotlight", journal = j-EULERIANA, volume = "2", number = "1", pages = "56--59", month = mar, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1024", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss1/8", abstract = "A spotlight on the Euler Archive focusing on Euler and the Basel Problem.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2022:VV, author = "Christopher Goff and Erik R. Tou", title = "Variety and Variation", journal = j-EULERIANA, volume = "2", number = "2", pages = "60--61", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1047", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/1", abstract = "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.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2022:RHM, author = "Erik R. Tou", title = "Review of {{\booktitle{The History of Mathematics: A Source-Based Approach}} (Vol. 2), Part I}", journal = j-EULERIANA, volume = "2", number = "2", pages = "62--66", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1043", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/2", abstract = "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.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Headley:2022:MCE, author = "Patrick T. Headley", title = "A Method for Calculating the Equation of Noon (an {English} translation of {{\booktitle{Methodus Computandi Aequationem Meridiei}}})", journal = j-EULERIANA, volume = "2", number = "2", pages = "67--78", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1034", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/3", abstract = "In this paper Euler presents a method for determining solar noon, the time at which the Sun crosses the meridian. The method requires the times of two observations of the Sun, one in the morning and one in the afternoon, at equal altitudes above the horizon. Solar noon is approximately the midpoint between two such observations, but, since the declination of the Sun will have changed during the day, a correction term, called the equation of noon, is required. Euler explains that this term is too large to ignore and discusses the table of values constructed by de la Hire; this table applies only at the latitude of Paris and relies on laborious calculations. For his own method, Euler describes the apparent motion of the Sun using spherical trigonometry and then uses differentials to complete the calculation with sufficient accuracy for his purposes. He provides examples and claims that his method makes it practical to construct a table at whatever latitude is required.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2022:MBP, author = "Sylvio R. Bistafa", title = "On the motion of boats propelled by oars in rivers", journal = j-EULERIANA, volume = "2", number = "2", pages = "79--93", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1046", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/4", abstract = "Euler considers the following problem: A boat with a perfect rudder moves at constant speed across a stream flowing in straight streamlines at assigned speeds. Assuming that the downstream velocity of the boat equals that of the river, how should the rudder be set so that the boat traverses a given path? He works out various instances, one of which gives rise to a variational problem, in detail. (From Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Barnett:2022:LMMb, author = "Janet H. Barnett and Dominic Klyve and Dave Ruch", title = "Learning Mathematics from the Master: A Collection of {Euler}-based Primary Source Projects for Today's Students, {Part II}", journal = j-EULERIANA, volume = "2", number = "2", pages = "94--106", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1044", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/5", abstract = "This article and its prequel 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 use.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{PhD:2022:EASb, author = "Cynthia Huffman", title = "{Euler Archive} Spotlight", journal = j-EULERIANA, volume = "2", number = "2", pages = "107--112", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1039", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/6", abstract = "This issue we spotlight the translations of Jordan Bell, one of the most prolific translators for the Euler Archive.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2022:AQC, author = "Alexander Aycock", title = "Answer to a question concerning {Euler}'s paper {{\booktitle{``Variae considerationes circa series hypergeometricas''}}}", journal = j-EULERIANA, volume = "2", number = "2", pages = "113--119", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1028", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/7", abstract = "We solve a problem concerning Euler's paper \booktitle{Variae considerationes circa series hypergeometricas} (\cite{E661}), as suggested by G. Faber in the preface to Volume 16,2 of the first series of Euler's \booktitle{Opera Omnia}. Our solution employs methods introduced by Euler at other places.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Hassler:2022:BPH, author = "Uwe Hassler and Mehdi Hosseinkouchack", title = "{Basel} Problem: Historical perspective and further proofs from stochastic processes", journal = j-EULERIANA, volume = "2", number = "2", pages = "120--130", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1032", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/8", abstract = "In this note, we offer a historical perspective on solutions of the Basel problem. In particular, we have a closer look at some of the less famous results by Euler E41 and provide a review of a selection of the assemblage of earlier proofs. Moreover, we show how to generate further proofs using Karhunen-Lo{\`e}ve expansions of stochastic processes.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2022:ENV, author = "Sylvio R. Bistafa", title = "{Euler}'s Navigation Variational Problem", journal = j-EULERIANA, volume = "2", number = "2", pages = "131--142", month = sep, year = "2022", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1045", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol2/iss2/9", abstract = "In a 1747 publication, \booktitle{De motu cymbarum remis propulsarum in fluviis} (\booktitle{``On the motion of boats propelled by oars in rivers''}), Leonhard Euler (1707--1783) works out various instances of a boat moving at constant speed across a stream flowing in straight streamlines at assigned speeds, in which one of these gives rise to a variational problem consisting of finding the quickest crossing path between two points on opposite side of the river banks, which is generally known as the navigation variational problem. This problem together with the well-known catenary and brachistochrone problems, are considered classical examples in the calculus of variations. Here, we shall present a brief account on Euler's recurrent interests in calculus of variations, mainly laid out in three publications that span between 1738 and 1744. Particular focus will be given to Euler's navigation variational problem. A brief account on Lagrange's contributions to variational calculus is also presented.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2023:EA, author = "Christopher Goff and Erik Tou", title = "{Euler}'s Anticipations", journal = j-EULERIANA, volume = "3", number = "1", pages = "1--2", month = mar, year = "2023", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1060", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/1", abstract = "Welcome to Volume 3 of Euleriana. This issue highlights occasions where Euler's work anticipated future results from other others, sometimes by decades or even centuries!", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{PhD:2023:AOT, author = "Cynthia Huffman", title = "Analytical Observations (Translation of {E326})", journal = j-EULERIANA, volume = "3", number = "1", pages = "3--22", month = mar, year = "2023", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1048", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/2", abstract = "Euler, in this publication with Enestr{\"o}m number E326, provides an induction fallacy which arises from analyzing a particular sequence. Euler wrote this work in 1763, one of only two papers he wrote on sequences and/or series in the 1760's, out of a total of 79 papers on series during his career. His goal in E326 is to investigate the middle terms in the expansion of powers of quadratic trinomial expressions, beginning with the specific simple quadratic, before considering the general quadratic. The induction fallacy shows up during the analysis of the simple case when Euler first finds an explicit formula for the middle terms, now known as central trinomial coefficients (see the Online Encyclopedia of Integer Sequences, https://oeis.org/A002426). He then investigates a recursive formula which involves pronic and Fibonacci numbers, resulting in two integer sequences which agree for the first nine terms and then disagree from the tenth term onward. [C. Edward Sandifer, How Euler Did It, Mathematical Association of America, 2007, p. 143--146.]", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Craig-Wood:2023:EFF, author = "Nick Craig-Wood", title = "{Euler} Found the First Binary Digit Extraction Formula for $ \pi $ in 1779", journal = j-EULERIANA, volume = "3", number = "1", pages = "23--30", month = mar, year = "2023", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1049", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/3", abstract = "In 1779 Euler discovered two formulas for $ \pi $ which can be used to calculate any binary digit of $ \pi $ without calculating the previous digits. Up until now it was believed that the first formula with the correct properties (known as a BBP-type formula) for this calculation was published by Bailey, Borwein and Plouffe in 1997.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2023:EDF, author = "Alexander Aycock", title = "{Euler} and the Duplication Formula for the Gamma-Function", journal = j-EULERIANA, volume = "3", number = "1", pages = "31--35", month = mar, year = "2023", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1050", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/4", abstract = "We show how the formulas in Euler's paper \booktitle{Variae considerationes circa series hypergeometricas} [4] imply Legendre's duplication formula for the $ \Gamma $-function. This paper can be seen as an Addendum to [2].", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Saclolo:2023:EVS, author = "Michael P. Saclolo", title = "{Euler} and {Venus}' Suspicious Moon", journal = j-EULERIANA, volume = "3", number = "1", pages = "36--41", month = mar, year = "2023", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1040", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/5", abstract = "This is a brief note on Leonhard Euler's published German translation from the French of two memoirs read by Armand Henri Baudouin de Gu{\'e}madeuc to the Paris Academy of Sciences in 1761 and published the same year. The memoirs report on observations made of the planet Venus, performed in Limoges, France by Jacques Montaigne, where he claimed to have detected a moon orbiting the Morning and Evening Star.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2023:EAS, author = "Erik R. Tou", title = "{Euler Archive} Spotlight", journal = j-EULERIANA, volume = "3", number = "1", pages = "42--44", month = mar, year = "2023", CODEN = "????", DOI = "https://doi.org/10.56031/2693-9908.1056", ISSN = "2693-9908", bibdate = "Tue Apr 18 09:56:27 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/6", abstract = "A survey of two translations posted to the Euler Archive in 2022.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2023:WSE, author = "Christopher Goff and Erik R. Tou", title = "The Wide Scope of {Euler}'s Work", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/1", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Headley:2023:MNM, author = "Patrick T. Headley", title = "On the Motion of the Nodes of the {Moon} and the Variation of its Inclination to the Ecliptic (an {English} translation of {{\booktitle{De Motu Nodorum Lunae Eiusque Inclinationis Ad Eclipticam Variatione}}})", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/2", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Ehlers:2023:SDE, author = "Georg Ehlers", title = "Solution of the {Diophantine} equation $ (m a a + n b b) = c d(m c c + n d d) $ using rational numbers", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/3", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2023:ELP, author = "Alexander Aycock", title = "{Euler} and the {Legendre} Polynomials", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/4", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2023:ESS, author = "Alexander Aycock", title = "On {Euler}'s Solution of the Simple Difference Equation", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/5", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2023:EFP, author = "Alexander Aycock", title = "{Euler}'s First Proof of {Stirling}'s Formula", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/6", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2023:EVA, author = "Sylvio R. Bistafa", title = "{Euler}'s Variational Approach to the Elastica", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/7", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Hassler:2023:PN, author = "Uwe Hassler", title = "Perfect Numbers", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/8", acknowledgement = ack-nhfb, articleno = "8", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Saclolo:2023:EAS, author = "Michael P. Saclolo", title = "{Euler Archive} Spotlight: Translations of {Euler}'s Works to Languages other than {English}", journal = j-EULERIANA, volume = "3", number = "2", pages = "??--??", month = "????", year = "2023", CODEN = "????", ISSN = "2693-9908", bibdate = "Fri Aug 25 10:52:40 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol3/iss2/9", acknowledgement = ack-nhfb, articleno = "9", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2024:NTM, author = "Christopher Goff and Erik Tou", title = "Number Theory and More", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/1", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2024:RA, author = "Erik R. Tou", title = "Research on Arithmetic: an {English} translation of {{\booktitle{Recherches d Arithm{\'e}tique}} By Joseph-Louis Lagrange, Nouveaux M{\'e}moires de l'Acad{\'e}mie royale des Sciences et Belles-Lettres de Berlin 1773 (1775), pp. 265--312}", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/2", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Ehlers:2024:CWF, author = "Georg Ehlers", title = "On the Cases in Which the Formula $ x^4 + k x x y y + y^4 $ Can Be Reduced to a Square", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/3", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2024:EHD, author = "Alexander Aycock", title = "{Euler} and Homogeneous Difference Equations with Linear Coefficients", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/4", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2024:EGS, author = "Alexander Aycock", title = "{Euler} and the {Gaussian} Summation Formula for the Hypergeometric Series", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/5", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Aycock:2024:EPF, author = "Alexander Aycock", title = "{Euler} and a Proof of the Functional Equation for the {Riemann} Zeta-Function He Could Have Given", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/6", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2024:EAS, author = "Christopher Goff", title = "{Euler} Archive Spotlight: Multiple Search Options", journal = j-EULERIANA, volume = "4", number = "1", pages = "??--??", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Wed May 15 16:38:03 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss1/7", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Goff:2024:LBL, author = "Christopher Goff and Erik Tou", title = "Looking Back and Looking Forward", journal = j-EULERIANA, volume = "4", number = "2", pages = "95--96", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/1", acknowledgement = ack-nhfb, articleno = "1", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{DAntonio:2024:HED, author = "Lawrence D'Antonio", title = "How {Ed} Did It --- a memorial conference to honor {Ed Sandifer}", journal = j-EULERIANA, volume = "4", number = "2", pages = "97--105", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/2", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Cleary:2024:ESR, author = "Rick Cleary", title = "{Ed Sandifer}: a Running Mathematician and Mathematical Runner", journal = j-EULERIANA, volume = "4", number = "2", pages = "106--107", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/3", acknowledgement = ack-nhfb, articleno = "3", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Ehlers:2024:ACW, author = "Georg Ehlers", title = "About the Cases in Which the Formula $ x^4 + m x x y y + y^4 $ Can be Reduced to a Square", journal = j-EULERIANA, volume = "4", number = "2", pages = "108--133", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/4", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Fortune:2024:VSE, author = "Reilly R. Fortune", title = "On the Vibration of Strings: an {English} Translation of {Leonhard Euler}'s `{{\booktitle{Sur la Vibration des Cordes}}}' {(E140)}", journal = j-EULERIANA, volume = "4", number = "2", pages = "134--148", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/5", acknowledgement = ack-nhfb, articleno = "5", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Bistafa:2024:TSL, author = "Sylvio R. Bistafa", title = "Translating scientific {Latin} texts with artificial intelligence: the works of {Euler} and contemporaries", journal = j-EULERIANA, volume = "4", number = "2", pages = "149--171", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/6", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", } @Article{Tou:2024:EAS, author = "Erik Tou", title = "{Euler} Archive Spotlight: {Ed Sandifer}'s Influence", journal = j-EULERIANA, volume = "4", number = "2", pages = "172--174", month = "????", year = "2024", CODEN = "????", ISSN = "2693-9908", bibdate = "Thu Sep 26 13:54:33 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/euleriana.bib", URL = "https://scholarlycommons.pacific.edu/euleriana/vol4/iss2/7", acknowledgement = ack-nhfb, articleno = "7", fjournal = "Euleriana", journal-URL = "https://scholarlycommons.pacific.edu/euleriana/", }