HOMOTECIA Nº 4-16 Abril 2018
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1 Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert
Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert Compiled and translated by Oscar Sheynin Berlin, 2010 Copyright Sheynin 2010 www.sheynin.de ISBN 3-938417-01-3 1 Contents Foreword I. Nicolaus Fuss, Eulogy on Leonhard Euler, 1786. Translated from German II. M. J. A. N. Condorcet, Eulogy on Euler, 1786. Translated from French III. Daniel Bernoulli, Autobiography. Translated from Russian; Latin original received in Petersburg in 1776 IV. M. J. A. N. Condorcet, Eulogy on [Daniel] Bernoulli, 1785. In French. Translated by Daniel II Bernoulli in German, 1787. This translation considers both versions V. R. Wolf, Daniel Bernoulli from Basel, 1700 – 1782, 1860. Translated from German VI. Gleb K. Michajlov, The Life and Work of Daniel Bernoullli, 2005. Translated from German VII. Daniel Bernoulli, List of Contributions, 2002 VIII. J. H. S. Formey, Eulogy on Lambert, 1780. Translated from French IX. R. Wolf, Joh. Heinrich Lambert from Mühlhausen, 1728 – 1777, 1860. Translated from German X. J.-H. Lambert, List of Publications, 1970 XI. Oscar Sheynin, Supplement: Daniel Bernoulli’s Instructions for Meteorological Stations 2 Foreword Along with the main eulogies and biographies [i, ii, iv, v, viii, ix], I have included a recent biography of Daniel Bernoulli [vi], his autobiography [iii], for the first time translated from the Russian translation of the Latin original but regrettably incomplete, and lists of published works by Daniel Bernoulli [vii] and Lambert [x]. The first of these lists is readily available, but there are so many references to the works of these scientists in the main texts, that I had no other reasonable alternative. -
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. -
Stefanie Ursula Eminger Phd Thesis
CARL FRIEDRICH GEISER AND FERDINAND RUDIO: THE MEN BEHIND THE FIRST INTERNATIONAL CONGRESS OF MATHEMATICIANS Stefanie Ursula Eminger A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in Research@StAndrews:FullText at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6536 This item is protected by original copyright Carl Friedrich Geiser and Ferdinand Rudio: The Men Behind the First International Congress of Mathematicians Stefanie Ursula Eminger This thesis is submitted in partial fulfilment for the degree of PhD at the University of St Andrews 2014 Thesis Declaration 1. Candidate’s declarations: I, Stefanie Eminger, hereby certify that this thesis, which is approximately 78,500 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for a higher degree. I was admitted as a research student in September 2010 and as a candidate for the degree of PhD in September 2010; the higher study for which this is a record was carried out in the University of St Andrews between 2010 and 2014. Date ……………… Signature of candidate …………………………………… 2. Supervisor’s declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of PhD in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree. -
History of Mathematics Clio Mathematicæ the Muse of Mathematical Historiography Craig Smorynski´
History of Mathematics Clio Mathematicæ The Muse of Mathematical Historiography Craig Smorynski´ History of Mathematics A Supplement 123 Craig Smorynski´ 429 S. Warwick Westmont, IL 60559 USA [email protected] ISBN 978-0-387-75480-2 e-ISBN 978-0-387-75481-9 Library of Congress Control Number: 2007939561 Mathematics Subject Classification (2000): 01A05 51-Axx, 15-xx c 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper. 987654321 springer.com Contents 1 Introduction ............................................... 1 1 An Initial Assignment . 1 2 AboutThisBook........................................ 7 2 Annotated Bibliography ................................... 11 1 General Remarks . 11 2 General Reference Works . 18 3 General Biography . 19 4 General History of Mathematics . 21 5 History of Elementary Mathematics . 23 6 SourceBooks........................................... 25 7 Multiculturalism . 27 8 Arithmetic ............................................. 28 9 Geometry .............................................. 28 10 Calculus................................................ 29 11 Women in Science . 30 12 MiscellaneousTopics..................................... 35 13 Special Mention . 36 14 Philately . -
Lambert's Proof of the Irrationality of Pi
Lambert’s proof of the irrationality of Pi: Context and translation Denis Roegel To cite this version: Denis Roegel. Lambert’s proof of the irrationality of Pi: Context and translation. [Research Report] LORIA. 2020. hal-02984214 HAL Id: hal-02984214 https://hal.archives-ouvertes.fr/hal-02984214 Submitted on 30 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Lambert’s proof of the irrationality of π: Context and translation this is a preliminary draft please check for the final version Denis Roegel LORIA, Nancy1 30 October 2020 1Denis Roegel, LORIA, BP 239, 54506 Vandœuvre-lès-Nancy cedex, [email protected] 2 3 In this document, I give the first complete English translation of Johann Heinrich Lambert’s memoir on the irrationality of π published in 1768 [92], as well as some contextual elements, such as Legendre’s proof [98] and more recent proofs such as Niven’s [109]. Only a small part of Lambert’s memoir has been translated before, namely in Struik’s source book [143]. My trans- lation is not based on that of Struik and it is supplemented with notes and indications of gaps or uncertain matters. -
Origin of Irrational Numbers and Their Approximations
computation Review Origin of Irrational Numbers and Their Approximations Ravi P. Agarwal 1,* and Hans Agarwal 2 1 Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., Kingsville, TX 78363, USA 2 749 Wyeth Street, Melbourne, FL 32904, USA; [email protected] * Correspondence: [email protected] Abstract: In this article a sincere effort has been made to address the origin of the incommensu- rability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of p2 and p. Ancient records substantiate that more than 5000 years back Vedic Ascetics were successful in approximating these numbers in terms of rational numbers and used these approximations for ritual sacrifices, they also indicated clearly that these numbers are incommensurable. Since then research continues for the known as well as unknown/expected irrational numbers, and their computation to trillions of decimal places. For the advancement of this broad mathematical field we shall chronologically show that each continent of the world has contributed. We genuinely hope students and teachers of mathematics will also be benefited with this article. Keywords: irrational numbers; transcendental numbers; rational approximations; history AMS Subject Classification: 01A05; 01A11; 01A32; 11-02; 65-03 Citation: Agarwal, R.P.; Agarwal, H. 1. Introduction Origin of Irrational Numbers and Their Approximations. Computation Almost from the last 2500 years philosophers have been unsuccessful in providing 2021, 9, 29. https://doi.org/10.3390/ satisfactory answer to the question “What is a Number”? The numbers 1, 2, 3, 4, , have ··· computation9030029 been called as natural numbers or positive integers because it is generally perceived that they have in some philosophical sense a natural existence independent of man. -
Stefanie Ursula Eminger Phd Thesis
CARL FRIEDRICH GEISER AND FERDINAND RUDIO: THE MEN BEHIND THE FIRST INTERNATIONAL CONGRESS OF MATHEMATICIANS Stefanie Ursula Eminger A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in Research@StAndrews:FullText at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6536 This item is protected by original copyright Carl Friedrich Geiser and Ferdinand Rudio: The Men Behind the First International Congress of Mathematicians Stefanie Ursula Eminger This thesis is submitted in partial fulfilment for the degree of PhD at the University of St Andrews 2014 Table of Contents Abstract 7 Acknowledgements 9 1. Introduction 11 2. Carl Friedrich Geiser (1843 – 1934) 15 2.1 Life 15 2.2 Connection with Steiner 33 2.3 Impact at the Polytechnic and on Education 39 3. Ferdinand Karl Rudio (1856 – 1929) 49 3.1 Life 49 3.2 Contribution to Euler’s Opera Omnia 53 4. The First International Congress of Mathematicians, Zurich 1897 57 4.1 Background and Organisation 57 4.1.1 Historical Developments 57 4.1.2 Organising the Congress 62 4.1.3 The Congress Itself 67 4.1.4 Geiser’s Contribution 76 4.1.5 Rudio’s Contribution 77 4.2 The Swiss Organising Committee 79 4.2.1 Ernst Julius Amberg (1871 – 1952) 79 4.2.2 Christian Beyel (1854 – 1941) 82 4.2.3 Hermann Bleuler (1837 – 1912) 83 4.2.4 Heinrich Burkhardt (1861 – 1914) 86 4.2.5 Fritz Bützberger (1862 – 1922) 89 4.2.5.1 Bützberger’s Work on Steiner 92 4.2.6 Gustave Dumas -
The Elementary Mathematical Works of Leonhard Euler (1707 – 1783) Paul Yiu Department of Mathematics Florida Atlantic University Summer 19991
The Elementary Mathematical Works of Leonhard Euler (1707 – 1783) Paul Yiu Department of Mathematics Florida Atlantic University Summer 19991 IA. Introduction to Euler’s Opera Omnia 1 IB. Solution of cubic equations 4 IC. Solution of quartic equations 5 IIA. Factorization of a quartic as a product of two real quadratics 7 IIB. Euler’s proof of the FTA for quartic polynomials 10 IIC. Relations between roots and coefficients 11 IIIA. Partial fraction decomposition 17 IIIB. Introduction to Introductio, I 20 IIIC. Exponentials and logarithms 21 IVA. Trigonometric functions 28 IVB. Logarithms of complex numbers 31 VA. Euler’s works on infinite series, introduction 35 VB. An example from Euler’s earliest paper on infinite series 38 VC. Euler’s Paper 72: Variae observationes circa series infinitas 39 1 1 1 ··· VIA. Euler’ first calculation of 1+22k + 32k + 42k + 43 VIB. Chapter X of Introductio, I 48 VIC. Euler’s “forgotten” paper Demonstration de la somme de cett suite 1 1 1 1 1+ 4 + 9 + 25 + 36 + ··· 49 VIIA. Jacob Bernoulli’s summation of the powers of natural numbers 54 VIIB. Euler’s summation formula 57 VIIC. Euler’s summation formula (continued) 59 VIIIA. The series expansions of cotangent, tangent, and secant 62 VIIIB. Euler’s constant γ 66 VIIIC. Summary on Bernoulli and Euler numbers 68 1Diagrams redrawn in August, 2007. I IXA. Continued fractions 69 IXB. Continued fractions and infinite series 73 IXC. Continued fraction expansion of functions 77 XA. Euler’s proof of Heron’s formula 80 XB. Area of a cyclic quadrilateral 81 XC. -
View This Volume's Front and Back Matter
Christopher Hollings HISTORY OF MATHEMATICS Y VOLUME 41 Mathematics Across the Iron Curtain A History of the Algebraic Theory of Semigroups https://doi.org/10.1090/hmath/041 HISTORY OF MATHEMATICS v VOLUME 41 Mathematics Across the Iron Curtain A History of the Algebraic Theory of Semigroups Christopher Hollings American Mathematical Society Providence, Rhode Island Editorial Board June Barrow-Green Bruce Reznick Robin Hartshorne Adrian Rice, Chair 2010 Mathematics Subject Classification. Primary 01A60, 20-03. For additional information and updates on this book, visit www.ams.org/bookpages/hmath-41 Library of Congress Cataloging-in-Publication Data Hollings, Christopher, 1982– Mathematics across the Iron Curtain : a history of the algebraic theory of semigroups / Christopher Hollings. pages cm. — (History of mathematics ; volume 41) Includes bibliographical references and indexes. ISBN 978-1-4704-1493-1 (alk. paper) 1. Semigroups. 2. Mathematics—History—20th century. 3. Cold War. I. Title. QA182.H65 2014 512.27—dc23 2014008281 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to [email protected]. -
Rudi Mathematici
Rudi Mathematici x4-8200x3+25213040x2-34452464000x+17652769695744=0 Rudi Mathematici January 1 1 T (1803) Guglielmo LIBRI Carucci dalla Sommaja USAMO 1997 – Problem 1 (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE Let ppp 321 ,,, be the prime numbers (1912) Boris GNEDENKO K (1822) Rudolf Julius Emmanuel CLAUSIUS 2 W listed in increasing order, and let x0 be a (1905) Lev Genrichovich SHNIRELMAN (1938) Anatoly SAMOILENKO real number between 0 and 1. For positive (1917) Yuri Alexeievich MITROPOLSHY 3 T integer k , define: 4 F (1643) Isaac NEWTON (1838) Marie Ennemond Camille JORDAN ⎧ if0 xk−1 = ,0 5 S (1871) Federigo ENRIQUES ⎪ (1871) Gino FANO xk = ⎨⎧ pk ⎫ ⎨ ⎬ if xk−1 ≠ ,0 6 S (1807) Jozeph Mitza PETZVAL ⎪ x (1841) Rudolf STURM ⎩⎩ k −1 ⎭ 2 7 M (1871) Felix Edouard Justin Emile BOREL (1907) Raymond Edward Alan Christopher PALEY where {x} denotes the fractional part of x . (1888) Richard COURANT 8 T (1924) Paul Moritz COHN Find, with proof, all x0 satisfying (1942) Stephen William HAWKING < x < 10 for which the sequence 9 W (1864) Vladimir Adreievich STELKOV 0 10 T (1875) Issai SCHUR xxx ,,, eventually becomes 0 . (1905) Ruth MOUFANG 210 K (1545) Guidobaldo DEL MONTE 11 F Why Astronomy is better than Sex: (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR If you get tired, wait ten minutes and try it again. 12 S (1906) Kurt August HIRSCH (1864) Wilhelm Karl Werner Otto Fritz Franz WIEN Statisticians 13 S (1876) Luther Pfahler EISENHART (1876) Erhard SCHMIDT What do you get when you cross a statistician with a chiropractor? 3 14 M (1902) Alfred TARSKI (1704) Johann CASTILLON You get an adjusted R squared from 15 T (1717) Mattew STEWART a BACKward regression problem. -
A Reader's Guide to Euler's Introductio
A Reader’s Guide to Euler’s Introductio V. Frederick Rickey Department of Mathematical Sciences United States Military Academy West Point, NY 10996 Email: [email protected] Abstract: Leonhard Euler’s Introductio in analysin infinitorum is surely one of his most famous works. For a century after its publication in 1748 it was widely read by aspiring mathematicians. Today, thanks to John Blan- ton, it is available in English translation. To encourage aspiring historians to read this famous work, a reader’s guide will be distributed. It will sum- marize the contents of the individual chapters of the Introductio, explain points that the reader might miss, point out antecedents of the work, and detail how the work influenced later mathematics. Prepared for the Euler 2K + 2 Conference. Countdown to the Tercentenary, Rumford Maine, 4-7 August 2002. The Introductio in analysin infinitorum (1748), by Leonhard Euler (1707–1783) is one of the most famous and important mathematical books ever written. Euclid’s Elements (300 BC) ranks supreme, and Newton’s Principia (1687) is the most famous scientific book ever written, but only partly deals with mathematics. Placing the Introductio second on the all time list in mathematics, may engender some arguments, but they will be interesting. That there have been 21 printings/editions in half a dozen languages certainly speaks highly of the importance of the Introductio. For many years I have been involved in seminars that took as their goal the reading of original mathe- matical texts. This has always been a rewarding experience and a synergistic one, for I have always learned more in the seminar setting than I ever could have learned on my own. -
Hurwitz's Complex Continued Fractions
Hurwitz’s Complex Continued Fractions A Historical Approach and Modern Perspectives. Dissertationsschrift zur Erlangung des naturwissenschaftlichen Doktorgrades der Julius-Maximilians-Universit¨at W¨urzburg vorgelegt von Nicola Oswald aus Kronach W¨urzburg 2014 2 ”Knowledge is in the end based on acknowledgement.” Ludwig Wittgenstein (1889 - 1951) Ich freue mich, an dieser Stelle die Gelegenheit zu nutzen, einigen Menschen zu danken, die mich w¨ahrend der letzten drei Jahre unterst¨utzt und begleitet haben. Mein erstes großes Dankesch¨on geb¨uhrt nat¨urlich J¨orn Steuding, der mir diese Promotionsstelle nicht nur erm¨oglicht hat, sondern mir seitdem als Betreuer stets mit Rat und Tat zur Hilfe steht. Er erm¨oglichte mir den Besuch zahlreicher Konferenzen, meine Forschungsinter- essen zu finden und selbstst¨andig eigene Projekte zu verwirklichen. In unserer gemein- samen Arbeitsgruppe zusammen mit Thomas Christ, sowie am Institut, genoss ich sehr die fortw¨ahrend freundliche und r¨ucksichtsvolle Atmosph¨are. Außerdem m¨ochte ich meinen Dank Karma Dajani aussprechen, die mir bereits zu Beginn meiner Arbeit erste Inspirationen zur Ergodentheorie gab. W¨ahrend ihres Aufen- thalts in W¨urzburg im Sommersemester 2014 hatte ich große Freude daran, dieses Inter- esse wieder aufzunehmen und konnte viel pers¨onliche Motivation aus ihrer herzlichen Art sch¨opfen. Im Bezug auf meine mathematik-historische Forschung m¨ochte ich mich ausdr¨ucklich bei meiner Mentorin Renate Tobies und Klaus Volkert bedanken. Beide halfen mir sehr bei meinem Einstieg in diesen neuen Fachbereich und ich bin ihnen f¨ur viele gute Ratschl¨age und Ermutigungen dankbar. In dieser Hinsicht sind auch das Archiv der ETH Z¨urich, insbesondere die hervorra- gende Betreuung von Evelyn Boesch, die Staats- und Universit¨atsbibliothek G¨ottingen, das Staatsarchiv Basel und das Universit¨atsarchiv Halle-Wittenberg zu erw¨ahnen.