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Downloaded from Brill.Com09/24/2021 10:06:53AM Via Free Access 268 Revue De Synthèse : TOME 139 7E SÉRIE N° 3-4 (2018) Chercheur Pour IBM
REVUE DE SYNTHÈSE : TOME 139 7e SÉRIE N° 3-4 (2018) 267-288 brill.com/rds A Task that Exceeded the Technology: Early Applications of the Computer to the Lunar Three-body Problem Allan Olley* Abstract: The lunar Three-Body problem is a famously intractable problem of Newtonian mechanics. The demand for accurate predictions of lunar motion led to practical approximate solutions of great complexity, constituted by trigonometric series with hundreds of terms. Such considerations meant there was demand for high speed machine computation from astronomers during the earliest stages of computer development. One early innovator in this regard was Wallace J. Eckert, a Columbia University professor of astronomer and IBM researcher. His work illustrates some interesting features of the interaction between computers and astronomy. Keywords: history of astronomy – three body problem – history of computers – Wallace J. Eckert Une tâche excédant la technologie : l’utilisation de l’ordinateur dans le problème lunaire des trois corps Résumé : Le problème des trois corps appliqué à la lune est un problème classique de la mécanique newtonienne, connu pour être insoluble avec des méthodes exactes. La demande pour des prévisions précises du mouvement lunaire menait à des solutions d’approximation pratiques qui étaient d’une complexité considérable, avec des séries tri- gonométriques contenant des centaines de termes. Cela a très tôt poussé les astronomes à chercher des outils de calcul et ils ont été parmi les premiers à utiliser des calculatrices rapides, dès les débuts du développement des ordinateurs modernes. Un innovateur des ces années-là est Wallace J. Eckert, professeur d’astronomie à Columbia University et * Allan Olley, born in 1979, he obtained his PhD-degree from the Institute for the History and Philosophy of Science Technology (IHPST), University of Toronto in 2011. -
Moon-Earth-Sun: the Oldest Three-Body Problem
Moon-Earth-Sun: The oldest three-body problem Martin C. Gutzwiller IBM Research Center, Yorktown Heights, New York 10598 The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler’s laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravitational attraction of both the Earth and the Sun. Newton discussed this problem at great length, and with mixed success; it was the only testing ground for his Universal Gravitation. This background for today’s many-body theory is discussed in some detail because all the guiding principles for our understanding can be traced to the earliest developments of astronomy. They are the oldest results of scientific inquiry, and they were the first ones to be confirmed by the great physicist-mathematicians of the 18th century. By a variety of methods, Laplace was able to claim complete agreement of celestial mechanics with the astronomical observations. Lagrange initiated a new trend wherein the mathematical problems of mechanics could all be solved by the same uniform process; canonical transformations eventually won the field. They were used for the first time on a large scale by Delaunay to find the ultimate solution of the lunar problem by perturbing the solution of the two-body Earth-Moon problem. -
A Task That Exceeded the Technology: Early Applications of the Computer to the Lunar Three-Body Problem *
A task that exceeded the technology: early applications of the computer to the lunar three-body problem * Allan Olley Abstract: The lunar Three-Body problem is a famously intractable aspect of Newto- nian mechanics. The demand for accurate predictions of lunar motion led to practical ap- proximate solutions of great complexity, constituted by trigonometric series with hundreds of terms. Such considerations meant there was demand for high speed machine computation from astronomers during the earliest stages of computer development. One early innovator in this regard was Wallace J. Eckert, a Columbia University professor of astronomer and IBM researcher. His work illustrates some interesting features of the interaction between computers and astronomy. Keywords: history of astronomy, three body problem, history of computers, W. J. Eckert *This is the submitted (ie unreviewed) version of this article, which appears in its official version at Revue de Synth`ese, Vol. 139, iss. 3-4, pp. 267-288 DOI: 10.1163/19552343-13900014 . Allan Olley, born in 1979, is an independent scholar, whose research focuses on the history of computers and celestial mechanics. ([email protected]) 1 The three body problem in astronomy consists of finding a general expression for the trajectory of three celestial bodies in mutual gravitational attraction. Unlike the two body problem that admits of a ready solution, the three body problem is famously intractable with no definitive solution for the general case and this has made it the focus of a great deal of intellectual effort. The first manifestation of these difficulties was Newton's attempts to use his theory of gravity to derive adequate predictions of the motion of the Moon. -
View This Volume's Front and Back Matter
Titles in This Series Volume 8 Kare n Hunger Parshall and David £. Rowe The emergenc e o f th e America n mathematica l researc h community , 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moore 1994 7 Hen k J. M. Bos Lectures in the history of mathematic s 1993 6 Smilk a Zdravkovska and Peter L. Duren, Editors Golden years of Moscow mathematic s 1993 5 Georg e W. Mackey The scop e an d histor y o f commutativ e an d noncommutativ e harmoni c analysis 1992 4 Charle s W. McArthur Operations analysis in the U.S. Army Eighth Air Force in World War II 1990 3 Pete r L. Duren, editor, et al. A century of mathematics in America, part III 1989 2 Pete r L. Duren, editor, et al. A century of mathematics in America, part II 1989 1 Pete r L. Duren, editor, et al. A century of mathematics in America, part I 1988 This page intentionally left blank https://doi.org/10.1090/hmath/008 History of Mathematics Volume 8 The Emergence o f the American Mathematical Research Community, 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moor e Karen Hunger Parshall David E. Rowe American Mathematical Societ y London Mathematical Societ y 1991 Mathematics Subject Classification. Primary 01A55 , 01A72, 01A73; Secondary 01A60 , 01A74, 01A80. Photographs o n th e cove r ar e (clockwis e fro m right ) th e Gottinge n Mathematisch e Ges - selschafft, Feli x Klein, J. J. Sylvester, and E. H. Moore. -
1954-06-06 University of Notre Dame Commencement Program
One Hundred Ninth Annual Commencement JUNE ExERCISES THE UNIVERSITY OF NOTRE DAME NoTRE DAME, INDIANA THE GRADUATE ScHOOL THE CoLLEGE OF ARTS AND LETTERS THE COLLEGE OF SCIENCE THE COLLEGE OF ENGINEERING THE CoLLEGE oF LAw THE CoLLEGE OF CoMMERCE In the University Stadium At 2:00p.m. (Central Daylight Time) June 6, 1954 PROGRAM Processional The Conferring of Degrees, by the Rev. Theodore M. Hesburgh, C.S.C., President of the University I ! Commencement Address, l l 1 by James Rhyne Killian, Jr., President of Massachusetts Institute of Technology The Blessing, by the Most Rev. Allen J. Babcock, I Bishop of Grand Rapids I National Anthem \ i Recessional l j Degrees Conferred The University of Notre Dame announces the conferring of: The Degree of Doctor of Laws, honoris causa, on: Most Reverend Allen J. Babcock, of Grand Rapids, Michigan Mr. Harold S. Vance, of South Bend, Indiana Honorable Ernest E. L. Hammer, of New York City Mr. Thomas W. Pangborn, Hagerstown, Maryland The Degree of Doctor of Literature, honoris causa, on: Mr. Samuel Eliot Morison, of Cambridge, Massachusetts The Degree of Doctor of Science, honoris causa, on: Mr. James Rhyne Killian, Jr., of Cambridge, Massachusetts IN THE GRADUATE SCHOOL The University of Notre Dame confers -the following degrees in course: The Degree of Doctor of Philosophy on: Clifford Scott Barker, Pittsburgh, Pennsylvania B.S., Carnegie Institute of Technology, 1948; M.S., University of Notre Dame, 1952. Major subject: Metallurgy. Dissertation: Study of the Kinetics of Order-Disorder Transformations. 3 Joseph Ming-shun Chiao, Hopie, China B.A., Catholic University of Peking (China}, 1939; M.A., Ibid., 1942. -
RM Calendar 2013
Rudi Mathematici x4–8220 x3+25336190 x2–34705209900 x+17825663367369=0 www.rudimathematici.com 1 T (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose (1912) Boris Gnedenko 2 W (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 F (1643) Isaac Newton RM071 5 S (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 1998-A1 (1871) Federigo Enriques RM084 (1871) Gino Fano A right circular cone has base of radius 1 and height 3. 6 S (1807) Jozeph Mitza Petzval A cube is inscribed in the cone so that one face of the (1841) Rudolf Sturm cube is contained in the base of the cone. What is the 2 7 M (1871) Felix Edouard Justin Emile Borel side-length of the cube? (1907) Raymond Edward Alan Christopher Paley 8 T (1888) Richard Courant RM156 Scientists and Light Bulbs (1924) Paul Moritz Cohn How many general relativists does it take to change a (1942) Stephen William Hawking light bulb? 9 W (1864) Vladimir Adreievich Steklov Two. One holds the bulb, while the other rotates the (1915) Mollie Orshansky universe. 10 T (1875) Issai Schur (1905) Ruth Moufang Mathematical Nursery Rhymes (Graham) 11 F (1545) Guidobaldo del Monte RM120 Fiddle de dum, fiddle de dee (1707) Vincenzo Riccati A ring round the Moon is ̟ times D (1734) Achille Pierre Dionis du Sejour But if a hole you want repaired 12 S (1906) Kurt August Hirsch You use the formula ̟r 2 (1915) Herbert Ellis Robbins RM156 13 S (1864) Wilhelm Karl Werner Otto Fritz Franz Wien (1876) Luther Pfahler Eisenhart The future science of government should be called “la (1876) Erhard Schmidt cybernétique” (1843 ). -
Rudi Mathematici
Rudi Mathematici x4-8188x3+25139294x2-34301407052x+17549638999785=0 Rudi Mathematici January 53 1 S (1803) Guglielmo LIBRI Carucci dalla Sommaja Putnam 1999 - A1 (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE Find polynomials f(x), g(x), and h(x) _, if they exist, (1912) Boris GNEDENKO such that for all x 2 S (1822) Rudolf Julius Emmanuel CLAUSIUS f (x) − g(x) + h(x) = (1905) Lev Genrichovich SHNIRELMAN (1938) Anatoly SAMOILENKO −1 if x < −1 1 3 M (1917) Yuri Alexeievich MITROPOLSHY 4 T (1643) Isaac NEWTON = 3x + 2 if −1 ≤ x ≤ 0 5 W (1838) Marie Ennemond Camille JORDAN − + > (1871) Federigo ENRIQUES 2x 2 if x 0 (1871) Gino FANO (1807) Jozeph Mitza PETZVAL 6 T Publish or Perish (1841) Rudolf STURM "Gustatory responses of pigs to various natural (1871) Felix Edouard Justin Emile BOREL 7 F (1907) Raymond Edward Alan Christopher PALEY and artificial compounds known to be sweet in (1888) Richard COURANT man," D. Glaser, M. Wanner, J.M. Tinti, and 8 S (1924) Paul Moritz COHN C. Nofre, Food Chemistry, vol. 68, no. 4, (1942) Stephen William HAWKING January 10, 2000, pp. 375-85. (1864) Vladimir Adreievich STELKOV 9 S Murphy's Laws of Math 2 10 M (1875) Issai SCHUR (1905) Ruth MOUFANG When you solve a problem, it always helps to (1545) Guidobaldo DEL MONTE 11 T know the answer. (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of (1906) Kurt August HIRSCH 12 W mathematics. -
RM Calendar 2010
Rudi Mathematici x4-8208x3+25262264x2-34553414592x+17721775541520=0 Rudi Mathematici January 1 F (1894) Satyendranath BOSE 4th IMO (1962) - 1 (1878) Agner Krarup ERLANG (1912) Boris GNEDENKO Find the smallest natural number with 6 as (1803) Guglielmo LIBRI Carucci dalla Sommaja the last digit, such that if the final 6 is moved 2 S (1822) Rudolf Julius Emmanuel CLAUSIUS to the front of the number it is multiplied by (1938) Anatoly SAMOILENKO 4. (1905) Lev Genrichovich SHNIRELMAN Gauss Facts (Heath & Dolphin) 3 S (1917) Yuri Alexeievich MITROPOLSHY 1 4 M (1643) Isaac NEWTON RM071 Gauss can trisect an angle with a straightedge 5 T (1871) Federigo ENRIQUES RM084 and compass. (1871) Gino FANO Gauss can get to the other side of a Möbius (1838) Marie Ennemond Camille JORDAN strip. 6 W (1807) Jozeph Mitza PETZVAL (1841) Rudolf STURM From a Serious Place 7 T (1871) Felix Edouard Justin Emile BOREL Q: What is lavender and commutes? (1907) Raymond Edward Alan Christopher PALEY A: An abelian semigrape. 8 F (1924) Paul Moritz COHN (1888) Richard COURANT The description of right lines and circles, upon (1942) Stephen William HAWKING which geometry is founded, belongs to 9 S (1864) Vladimir Adreievich STELKOV mechanics. Geometry does not teach us to 10 S (1905) Ruth MOUFANG draw these lines, but requires them to be (1875) Issai SCHUR drawn. 2 11 M (1545) Guidobaldo DEL MONTE RM120 Isaac NEWTON (1734) Achille Pierre Dionis DU SEJOUR (1707) Vincenzo RICCATI 12 T (1906) Kurt August HIRSCH Mathematics is a game played according to 13 W (1876) Luther Pfahler EISENHART certain simple rules with meaningless marks (1876) Erhard SCHMIDT on paper. -
A Bibliography of Collected Works and Correspondence of Mathematicians Steven W
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by eCommons@Cornell A Bibliography of Collected Works and Correspondence of Mathematicians Steven W. Rockey Mathematics Librarian Cornell University [email protected] December 14, 2017 This bibliography was developed over many years of work as the Mathemat- ics Librarian at Cornell University. In the early 1970’s I became interested in enhancing our library’s holdings of collected works and endeavored to comprehensively acquire all the collected works of mathematicians that I could identify. To do this I built up a file of all the titles we held and another file for desiderata, many of which were out of print. In 1991 the merged files became a printed bibliography that was distributed for free. The scope of the bibliography includes the collected works and correspon- dence of mathematicians that were published as monographs and made available for sale. It does not include binder’s collections, reprint collec- tions or manuscript collections that were put together by individuals, de- partments or libraries. In the beginning I tried to include all editions, but the distinction between editions, printings, reprints, translations and now e-books was never easy or clear. In this latest version I have supplied the OCLC identification number, which is used by libraries around the world, since OCLC does a better job connecting the user with the various ver- sion than I possibly could. In some cases I have included a title that has an author’s mathematical works but have not included another title that may have their complete works. -
Ernest William Brown 1866-1938
NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA BIOGRAPHICAL MEMOIRS VOLUME XXI SIXTH MEMOIR BIOGRAPHICAL MEMOIR OF ERNEST WILLIAM BROWN 1866-1938 BY FRANK SCHLESINGER and DIRK BROUWER PRESENTED TO THE ACADEMY AT THE AUTUMN MEETING, 1939 ERNEST WILLIAM BROWN 1866-1938 BY FRANK SCHLESINGER AND DIRK BROUWER Ernest William Brown's forbears on both sides lived at Hull, England, or in its immediate neighborhood. His father's father, William Brown (born 1806) was in early life a sailor, later a ship owner and a ship broker. His father (1837-1893), also named William, was for part of his life a farmer and later a lumber merchant. In 1863 he married Emma Martin (1839- 1870), by whom he had four children, two boys and two girls. Of these Ernest (1866 November 29 to 1938 July 22) was the second oldest. In 1870 a scarlet fever epidemic carried off his mother and his younger brother. Ernest was not quite four years old at this time and he and his two sisters were looked after by a maiden aunt for about five years, when his father married again. When Ernest was six years old he began to attend a day school in Hull. The master was at once impressed by his talent for music and urged his father to let the boy prepare for a musical career. This plan seems to have been given serious consideration; and later Ernest, and his elder sister Ella, studied the piano under the guidance of their step-mother. But later his tastes turned toward mathematics in which he greatly excelled both at the day school and at the Hull and East Riding College. -
The Charles S. Peirce-Simon Newcomb Correspondence
The Charles S. Peirce-Simon Newcomb Correspondence Carolyn Eisele Proceedings of the American Philosophical Society, Vol. 101, No. 5. (Oct. 31, 1957), pp. 409-433. Stable URL: http://links.jstor.org/sici?sici=0003-049X%2819571031%29101%3A5%3C409%3ATCSPNC%3E2.0.CO%3B2-L Proceedings of the American Philosophical Society is currently published by American Philosophical Society. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/amps.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Tue Mar 11 07:51:41 2008 THE CHARLES S. -
Simon Newcomb Papers [Finding Aid]. Library of Congress. [PDF Rendered
Simon Newcomb Papers A Finding Aid to the Collection in the Library of Congress Manuscript Division, Library of Congress Washington, D.C. 2014 Contact information: http://hdl.loc.gov/loc.mss/mss.contact Additional search options available at: http://hdl.loc.gov/loc.mss/eadmss.ms014072 LC Online Catalog record: http://lccn.loc.gov/mm79034629 Prepared by Manuscript Division Staff Collection Summary Title: Simon Newcomb Papers Span Dates: 1813-1949 Bulk Dates: (bulk 1865-1909) ID No.: MSS34629 Creator: Newcomb, Simon, 1835-1909 Extent: 46,000 items ; 145 containers plus 8 oversize ; 61.2 linear feet Language: Collection material in English Location: Manuscript Division, Library of Congress, Washington, D.C. Summary: Astronomer, mathematician, and economist. Correspondence, diaries, commonplace books, drafts of speeches, articles, reviews, and books, financial papers, genealogical papers, charts, tables, computations, photos, and printed matter reflecting Newcomb's personal and family life, his work in mathematics and astronomy, his writing of articles for encyclopedias and other publications, and his work as president of the International Congress of Arts and Sciences. Selected Search Terms The following terms have been used to index the description of this collection in the Library's online catalog. They are grouped by name of person or organization, by subject or location, and by occupation and listed alphabetically therein. People Barnard, Edward Emerson, 1857-1923--Correspondence. Bell, Alexander Graham, 1847-1922--Correspondence. Boss, Lewis, 1846-1912--Correspondence. Burnham, S. W. (Sherburne Wesley), 1838-1921--Correspondence. Campbell, William Wallace, 1862-1938--Correspondence. Cattell, James McKeen, 1860-1944--Correspondence. Davidson, George, 1825-1911--Correspondence. Gill, David, 1843-1914--Correspondence.