@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"
}
@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/|"}
@String{j-EULERIANA = "Euleriana"}
@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/",
}
