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Premium member Presentation Transcript The Euler Archive: : The Euler Archive: Illuminating the Life and Times of Leonhard Euler http://www.EulerArchive.org Lee Stemkoski Adelphi University April 16, 2007 Leonhard Euler : Leonhard Euler A Leading Scholar of the 18th Century (1707 – 1783) Quantity of work (850+) Breadth of topics Depth of investigation Presentation style Outline of Topics : Outline of Topics A history of publishing Euler’s works The Euler Archive: history, layout Life in Basel, St. Petersburg, Berlin Some of Euler’s major contributions Euler’s continuing influence Publishing Euler’s works : Publishing Euler’s works 1830: St. Petersburg Academy “finishes” backlog of Euler’s works 1843: P.H. Fuss creates index Fuss-Jacobi correspondence 1849: Commentationes Arithmeticae 1883: F. Rudio delivers biographical talk 1896: Hagen creates updated index The Euler Commission : The Euler Commission April, 1908: International Mathematical Congress discusses publication Previously discussed in 1907: - International Association of Academies - Swiss Society of Natural Sciences August, 1908: Euler Commission created 1910: Eneström creates updated index 1911: Opera Omnia publication begins Worldwide Support : Worldwide Support Subscriptions Academies of Paris, Berlin, and St. Petersburg each order 40 sets Donations German Association of Mathematicians American Mathematical Society Euler’s Opera Omnia : Euler’s Opera Omnia Series I: Mathematics (29/29) Series II: Mechanics, Astronomy (29/31) Series III: Physics, Miscellaneous (12/12) Series IVA: Correspondence (4/10) Series IVB: Manuscripts and Notebooks The Euler Archive: History : The Euler Archive: History 2001: The Euler Society Dr. Edward Sandifer, talk at Dartmouth Two graduate students: Klyve, Stemkoski 2002: Conference presentation 2003: Euler Archive, version 1.0 Primarily a response to inaccessibility of Euler’s works (cost and location) Marianne Gerber, Deputy Consul, SHARE The Euler Archive: Layout : The Euler Archive: Layout One webpage for each of Euler’s works Organization: Subject, Date, Journal Context: History, Biography, Academies, Contemporaries, Miscellaneous Features: Translations, Letters, Resources The Life and Times ofLeonhard Euler : The Life and Times ofLeonhard Euler Primary Sources: Autobiography Eulogy by Nicolaus Fuss Eulogy by Marquis de Condorcet Correspondence The Basel Period : The Basel Period Born: April 15, 1707 - Basel, Switzerland Parents, Religion, and Mathematics 1720: enters University of Basel 1722: prima laurea (~ Bachelor of Arts) 1723: magister (~ Master of Arts) Johann Bernoulli: no lessons, only questions Friends: Daniel and Nicolaus Bernoulli, Johann Kaspar Wettstein Search for Employment : Search for Employment 1725: young Bernoulli brothers leave for the new St. Petersburg Academy; Euler offered professorship of medicine 1726: applies for professor of physics at University of Basel 1727: leaves for St. Petersburg Paris Prize Competition – essay on masting of ships wins honorable mention The St. Petersburg years : The St. Petersburg years Death of Empress Catherine I Christian Goldbach and Number Theory 1733: Succeeds Daniel Bernoulli as professor of mathematics Jan. 1734: marries Katherina Gsell Nov. 1734: birth of Johann Albrecht The St. Petersburg years:early mathematics : The St. Petersburg years:early mathematics 1732: Fermat numbers [E-26] 3, 5, 17, 257, 65537, 4294967297 1734: Mixed partial derivatives [E-44] 1734: Functional notation f(x) [E-45] The Basel Problem : The Basel Problem In 1735: [E-41] The sum of the series 1/1 + 1/4 + 1/9 + 1/16 + 1/25 + … is exactly equal to π2 / 6. Bridges of Königsberg : Bridges of Königsberg In 1735: [E-53] Can you arrange a route that crosses every bridge exactly once? Academy Duties : Academy Duties Examination board member of academic gymnasium Weights and measures commission Development of hydraulic machines Cartography : Cartography 1735: Euler and Delisle direct the academy’s Department of Geography 1753: Preface to Geographic Atlas 1775: on the mathematics of projections Paris Prize Competition : Paris Prize Competition Euler: 18 total entries (12 wins) Sample topics: 1727: masting of ships 1738: properties of fire 1740: tides 1747: determining time from observations 1748: magnets 1748: movement of Jupiter and Saturn 1753: movement of ships without wind Major Works during firstSt. Petersburg period : Major Works during firstSt. Petersburg period 1736: Mechanics [E-15][E-16] 1739: Music Theory [E-33] 1738/1740: Arithmetic [E-17][E-35] Move to Berlin (1741) : Move to Berlin (1741) Political tensions in St. Petersburg Growing Family: Johann Albrecht, Karl, Katharina, Christoph, Charlotte, … Correspondence continues Russian Lodgers/Students: Razumovsky, Kotelnikov, Rumovsky Major Works in Berlin : Major Works in Berlin 1744: Calculus of Variations 1745: New Principles of Gunnery 1748: Introduction to the Analysis of the Infinite 1749: Theory of Ships 1753: Theory of Lunar Motion 1755: Differential Calculus 1762: Construction of Achromatic Lenses 1765: Theory of the Motion of Solid Bodies Introductio : Introductio 1748 [E-101] Variables and functions Polynomials and algebraic functions Exponents and logarithms Trigonometry Series Polyhedral Formula : Polyhedral Formula 1750-1751 [E-230] V = # vertices (corners) E = # edges F = # faces Then: V – E + F = 2 Euler-Fermat Theorem : Euler-Fermat Theorem 1760 [E-271] Choose integer a and prime number p ap – 1 (mod p) = 1 Replace p by arbitrary number n aφ(n) (mod n) = 1 Basis of many encryption algorithms End of Berlin period : End of Berlin period Fredrick the Great Maupertuis Return to St. Petersburg (1766) Major Works from Euler’ssecond St. Petersburg period : Major Works from Euler’ssecond St. Petersburg period 1768: Letters to a German Princess 1768: Integral Calculus 1769: Optics 1770: Algebra 1772: Theory of Lunar Motion 1773: Complete Theory on the Construction and Maneuvering of Ships Letters to a German Princess : Letters to a German Princess First published in 1768 (234 letters) General science: gravity, cosmos, tides Philosophy: the spirit, religion, morality, foundations of knowledge Physics: electricity, magnetism, telescopes, microscopes Over 40 editions by 1840 Euler’s final day : Euler’s final day Assistants Fuss and Lexell present Discussions about height of hot-air balloons orbit of planet Uranus Suffered a stroke in the early evening Euler’s continuing influence : Euler’s continuing influence Disciples / Students J.A. Euler, Fuss, Lexell, Rumovsky, … Style of presentation Legacy of publications Conclusion : Conclusion From the Eulogy written by Fuss: “What is there left … except our tender and eternal gratitude … [Euler] was worthy of admiration as much for his rare virtues as for the astonishing force of his genius.” You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.