Volume 2, number 1 May, 2003 |
Visit The Euler Society home page at http://www.eulersociety.org. |

**Fred
Rickey Gives First Euler Lecture**

Professor
V. Frederick Rickey of the United States Military Academy at West Point
delivered the First Euler Lecture on the morning of August 5, 2002 at the E2K+2
conference in Rumford, Maine. Fred
titled his talk “A Reader’s Guide to Euler’s *Introductio.*”

Fred
began by setting the stage for the publication of the *Introductio in
analysin infinitorum *in 1748. That
was the same year that Maria Agnesi published her best known work, also an
introduction to the mathematics one ought to know in order to learn calculus.
(An English edition of Agnesi’s book is barely visible on the projection screen
in the picture above.) When they
studied calculus, Leibniz and the older Bernoullis studied the variable
geometric properties of curved lines.
Euler, in his *Introductio*, changed the object being studied from
curves to functions, a major shift in the paradigms of mathematics.

Fred
turned to describing how to read the *Introductio*. He encourages a reader to look for the
Context, the Content and the Effect of any reading of an original mathematical
text. He needs Agnesi to help give the
context of the *Introductio*. The
content, he says, is a summary of the work itself. We find the effect when we find where later works derive from the
*Introductio*.

Next,
Fred changed his definition of the expression “how to read the *Introductio*”
and gave us a short lesson in how to read Latin. He says that he reads Latin with an English dictionary, not a
Latin dictionary, and demonstrated his technique, using passages from the *Introductio*
itself.

During
question time, Fred suggested forming a “Slow Reading Group” that would read
and discuss the *Introductio* slowly and carefully, over the course of
many months.

Fred bravely stepped into the role of First Euler Lecturer when the Chancellor of The Euler Society, Ron Calinger, fell ill in early July and was unable to attend the Conference. Ron seems to have recovered. People who were in the New York area on October 2 were able to attend the Pohle Colloquium heard the talk Ron would have given.

**At
the Bookstore**

*June
8, 2004: Venus in Transit*, by Eli Maor

Eli Maor is a talented writer of popular mathematics and scientific books. This little volume is about a relatively infrequent astronomical phenomenon, a so-called Transit of Venus, when the disk of Venus passes directly between the Earth and the Sun. Transits tend to occur either 8 years apart or 105 or 121 years apart, in patterns and for reasons described in detail in the book. An eight-year pair is about to occur, in June of 2004 and again in June of 2012.

The pair of 1761 and 1769 was of great importance in the history of science. They gave scientists their first good opportunity to measure the distance from the Earth to the Sun. The 1761 Transit occurred in the middle of the Seven Years War. Nevertheless, France and England managed a small bit of cooperation in trying to take observations of the Transit around the world, and so to use parallax to estimate the distance. The effort had reasonable success, and involved such notables as Mason and Dixon, who later achieved fame in America as surveyors. It was the world’s first significant effort at international scientific cooperation.

In 1769, Euler helped coordinate a similar international effort, though Maor mostly omits this aspect of the story. Euler sent a Russian expedition to Siberia headed by one of the political thorns in his side, but chose his son Charles to lead the expedition to take observations at the resorts on the Black Sea. It sometimes pays to get along with the boss.

Maor
does his usual good job of simplifying the mathematical concepts, especially
ideas like *nodes* and how they make it so that Transits of Venus can
occur only in June and December. The
mathematical reader will get more out of the book by checking the calculations
as much as possible.

The book is a little short on Euler, but it is a good account of the scientific and astronomical issues of his time.

186 pages. ISBN 0-691-04874-6. Princeton University Press, 2000.

*Gamma:
Exploring Euler’s Constant*, by Julian Havil

Euler
described the value we now call *gamma* as the difference between two
infinities, the infinite sum of the harmonic series and the natural logarithm
of infinity. The issue came up in the
1730’s as he was developing what we now call Euler-Maclaurin series, the
subject of David Pengelley’s talk at last summer’s Euler Conference.

Most
mathematics students know, or at least have heard, the definition of *gamma*. Some even believe their professors when the
professors say, “*Gamma* is important and interesting.” Few learn why. Havil tells us.

The book is rather technical, lots of summation signs, a few graphs and integral signs, and even a continued fraction and some infinite products. The mathematics, though, is mostly elementary, in the sense that it involves mostly topics in calculus, with a little from number theory and complex variables. It is, however, often intricate, so readers had best keep a pencil and more than a scrap of paper handy.

Over
the last few years, we’ve seen books on e, pi, i, zero and now *gamma*. What’s left?

266 pages. ISBN 0-691-09983-9. Princeton University Press. 2003.

**In
the Treasure Room**

*The
Euler-Mayer Correspondence (1751-1755)* by Eric G. Forbes

Those
of you who read Dava Sobol’s excellent book *Longitude* a few years ago
might remember the name of Johann Tobias Mayer, an also-ran in the race to
determine longitude at sea. Mayer got a
consolation price from the English Parliament for his excellent lunar tables. The plan was that if you could know exactly
where the moon was, then you could determine time by observing when the disk of
the moon passes in front of certain stars.
Then, you could compare the actual time to the observed local time and
determine longitude. People who pursued
this plan for determining longitude were derided as “Lunarians.”

Mayer’s success in calculating lunar tables depended in part on Euler’s work. This book describes what Mayer did, and gives annotated translations of the correspondence that passed between them between 1751 and 1755. They dealt with difficult mathematical and astronomical problems; it doesn’t make much sense without Forbes’ excellent commentary.

According to Craig Waff, this book has long (about 32 years now) been a standard among historians of astronomy. We Eulerians should know about it, too. My copy cost $50 0n eBay, but it’s widely available on InterLibrary Loan, too.

115 pages. ISBN 0-444-19580-7. American Elsevier Publishing, New York. 1971.

**Upcoming
Events**

The Euler Society’s next big event is scheduled for Roger Williams University in Newport, Rhode Island, August 10-13, 2003. Activities will begin with a reception the evening of Sunday, August 10.

Roger Williams is actually in Bristol, but we’re meeting at their conference center on the other side of the New Hope Bridge in Newport. See the announcement at the end of the Newsletter about how to register. Abstracts, or at least solemn promises to send abstracts, were due May 1, but because the Editor has procrastinated until after the Halifax meeting of the CSHPM, we can actually accept abstracts until June 7. Send abstracts to Ed Sandifer at esandifer@earthlink.net.

We already have abstracts, or at least solemn promises to deliver them soon, from

Ed Sandifer

Fred Rickey

Larry d’Antonio

Rob Bradley

John Glaus

Sam Kutler

Ron Calinger

Craig Waff

Stacy Langton

The Euler Society calls for papers to be presented at the Euler 2003 Conference, August 4-7, 2002 (See below). Send proposals (title, abstract, presenter and contact information) to esandifer@earthlink.net by June 7, 2003.

The Newsletter will gladly include short contributions about Euler, his life, works and influence, and we will provide links to longer contributions. Contact the Editor at esandifer@earthlink.net.

The
Mission of **The Euler Society** is threefold: It encourages scholarly
contributions examining the life, research, and influence of Leonhard
Euler. In part, these will be set
within his times, that is, within the Enlightenment, the rise to European power
status of Russia and Prussia, and the growth of royal science academies. **The Euler Society** will also explore
current studies in the mathematical sciences that build upon his thought. And it will promote translations into
English of selections from his writings, including correspondence and
notebooks, in leading up to the tercentenary of his birth in 2007.

Chancellor Ronald Calinger Catholic University calinger@cua.edu

President Robert Bradley Adelphi University bradley@panther.adelphi.edu

Vice President Ruediger Thiele University of Leipzig thieler@medizin.uni-leipzig.de

Secretary Edward Sandifer Western Connecticut State University esandifer@earthlink.net

Treasurer Mary Ann McLoughlin College of St Rose mcloughm@strose.edu

Ombudsman (ex officio) John Glaus The Euler Society restinn@midmaine.com

Euler 2003 Conference

__Countdown to the Tercentenary__

**Sunday,
August 10 – Wednesday, August 13, 2003**

**Roger
WILLIAMS UNIVERSITY, Bristol, Rhode Island**

** **

** The 2003 Euler conference will
be held at the Roger Williams University Residence and Conference Center. This
facility is located just minutes from historic Bristol and the excitement of
Newport. During E2k+3 you will be
accommodated in the conference center’s luxury bedrooms including
satellite TV, in-room coffee, individual climate control and dry cleaning
services. The Center also offers an indoor heated pool, sauna and fitness
center facility. **

** **

**Directions:**

** Roger Williams University Residence and
Conference Center in Portsmouth, is located 1.5 miles from the University’s
main campus in Bristol and about 12 miles North of the picturesque Newport
beaches, quaint shopping villages and historic mansions. **

** **

**Rates:**

** For all four days $329.00 **

** Includes: Luxury accommodations,
Breakfast, Lunch and Morning and Afternoon refreshment breaks.**

** **

** Day Meeting PACKAGE: $29.00 per day**

** Includes: Breakfast, Lunch and Morning
and Afternoon refreshment breaks.**

** **

** There is a $50.00 Registration fee to be
made payable to The Euler Society**

** **

**Please
make your reservations directly with:**

**Lorie Proulx**

**Roger Williams University
Residences and Conference CENTER: lproulx@rwu.edu
or www.rwu.edu**

** **

**Call
for Papers:**

** Abstracts are past due to Ed Sandifer,
but he hasn’t made the program yet, so you can still email him until Saturday,
June 7 at esandifer@earthlink.net
with your title.**

** **

**Blurb:**

** ****Last
year’s attendees came from Kyoto, Oxford, West Point, Cornell, Miami, Western
Connecticut, New Mexico, San Diego, Maine, and elsewhere. They unanimously agreed that the Euler
Conference was the best meeting they had ever attended. Expect Newport to be just as great.**

** **