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Origin and Interaction of Mathematics and Mechanics

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Origin and Interaction of Mathematics and Mechanics Jan Awrejcewicz Vadim A. Krysko Origin and Interaction of Mathematics and Mechanics Jan Awrejcewicz Technical University of Łódź Department of Automatics and Biomechanics 1/15 Stefanowskiego St. 90-924 Łódź, Poland e-mail: [email protected] www.p.lodz.pl/k16 Vadim A. Krysko Saratov State Technical University Department of Higher Mathematics 77 Polytechnicheskaya St. 410054,Saratov, Russia e-mail: [email protected] ISBN 83-911746-7-0 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Department of Automatics and Biomechanics, 1/15 Stefanowskiego St. 90-924 Łódź, Poland), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of informa- tion 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 property rights. © Department of Automatics and Biomechanics Press, 2007. Printed in Poland Publisher: Department of Automatics and Biomechanics, The Technical University of Łódź, 1/15 Stefanowski St., 90-924 Łódź, Poland Cover design: Marek Kaźmierczak Contents Foreword .............................................................................................1 1. The Beginning ..........................................................................7 2. The Alexandrian Library......................................................29 3. Ancient Rome .........................................................................39 4. Christianity.............................................................................55 5. Islam........................................................................................69 6. Dawn .......................................................................................79 7. First Universities and Academies .........................................87 th 8. The 19 century – the Quickening .....................................115 th 9. The 20 century – the Exponential Development .............135 10. The Worldwide Web............................................................167 11. Selected Biographies of Great Engineers and Mathematicians....................................................................185 Galileo Galilei (1564 – 1642) ................................................................................. 186 Johannes Kepler (1571 – 1630) ............................................................................. 188 Isaac Newton (1642 – 1727)................................................................................... 190 Gottfried Wilhelm von Leibniz (1646 – 1716) ..................................................... 193 Leonhard Euler (1707 – 1783)............................................................................... 197 Alexis Claude Clairaut (1713 – 1765)................................................................... 200 Jean Le Rond d’Alembert (1717 – 1783) ............................................................. 201 Joseph Louis Lagrange (1736 – 1813) .................................................................. 203 Pierre Simon de Laplace (1749 – 1827)................................................................ 205 Carl Friedrich Gauss (1777 – 1855)...................................................................... 208 Henri Poincaré (1854 – 1912)................................................................................ 210 Alexander Mikhailovich Lapunov (1857 – 1917) ................................................ 212 Vladimir Andreevich Steklov (1864 – 1926)........................................................ 214 Balthazar Van der Pol (1889 – 1959).................................................................... 218 Alexander Alexandrovich Andronov (1901 – 1952)............................................ 220 Nikolai Mitrofanovich Krilov (1879 – 1955)........................................................ 222 Nikolai Nikolayevich Bogolubov (1909 – 1992) ................................................... 223 Yuri Alexandrovich Mitropolski (born 1917) ..................................................... 225 Stefan Prokofeevich Timoshenko (1878 –1972)................................................... 227 Vasili Zakharovich Vlasov (1906 – 1958)............................................................. 232 Afterword........................................................................................235 Bibliography....................................................................................237 Author Biografical Sketches..........................................................241 ⎯ I ⎯ ⎯ II ⎯ List of illustrations “God created the World with numbers and Claudius Ptolemy; medieval image .................. 33 measure”; Wiliam Blake, “Europe”. ............1 Map of the world, with meridians and “The Thought”; Auguste Rodin. .........................7 parallels, according to Claudius Egypt during the pharaohs’ times; natural Ptolemy (179-100 BC). ............................. 34 resources.......................................................7 Map of the world according to Herodotus Mesopotamia (3PPrdPP - 2PPndPP mill. BC) (ab. 489-ab. 425 BC). ................................ 34 states and routes of migrations.....................8 Map of the world according to Eratosthenes Egyptian parchment with a fraction table............8 (ab. 276-196 BC)....................................... 34 Fragment of “Rhind’s Papyrus”; Eratosthenes of Cyrene; image from antiquity. .... 35 17PPthPP cent. BC; Egypt..............................9 Caesar; antic bust.............................................. 37 Nefertete; bust from Tell-el-Amarinah............10 She-Wolf of the Capitoline feeding Remus Example of early Hindu numerical notation. ....11 and Romulus, 6PPthPP century BC ............. 39 Paleolithic bones with numerical carvings; Roman Empire:natural resources and the beginnings of quinary system are economical relations.................................. 40 visible.........................................................11 Pont du Gard, the Roman aqueduct that Temple of Marduk in Babylon, ab.580 BC, provided water supplies for Nimes; model, Berlin, National Museum. ..............12 1PPstPP cent. BC, France ............................ 42 Ishtar Temple’s west towers; Babylon. .............13 Caracalla’s baths............................................... 42 Semiramis’ Gardens; artistic vision, Today’s view on Caracalla’s baths................... 43 19PPthPP cent...............................................13 Model of ancient Rome from the Museum Pythagoras; medieval image..............................15 of Roman Civilisation. .............................. 45 Pythagorean pentagram. ....................................18 Hadrian’s Mausoleum – today the Castle of Archytas of Tarentum; medieval vision. ...........19 Saint Angel; reconstruction from the Plato; ancient bust. ............................................20 Museum of Roman Civilisation................. 46 Athens in antiquity, after Pericles’ times; Publius Elius Hadrian, 2PPndPP cent. A.D......... 46 reconstruction of the city plan....................20 Marcus Ulpius Traian; 2PPndPP cent. A.D., Mausoleum in Halicarnassus; Louvre. Paris. ............................................ 46 reconstruction.............................................21 Plan of Rome from the early times to the Hermes with infant Dionysius; Praxiteles, Empire times; reconstruction..................... 47 the 4PPthPP cent. BC, Olympia Museum, The Pantheon; reconstruction. .......................... 48 Greece ........................................................21 The Colosseum; reconstruction from the Greek world during the Philip IIPPndPP’s Museum of Roman Civilisation................. 48 wars. ...........................................................22 The Pantheon – the dome’s section. ................. 49 Alexander of Macedon; Lysippus; Istanbul The Pantheon - inside. ...................................... 49 Museum......................................................23 Market gate in Miletus; Berlin Museum........... 53 Arsistotle; marble head; antiquity. ....................23 Plato’s Academy; mosaic from a Roman Alexander of Macedon’s conquests. .................25 house in Pompei. ....................................... 53 Hellenic countries built on the ruins of Christ; The Church of God’s Wisdom, Alexander the Great’s Empire....................26 Constantinople........................................... 55 Alexander the Great on his beloved Augustus as Pontifex Maximus; antique Bucephalus during the battle of Issos; bust ............................................................ 56 mosaic from Pompei. .................................26 “Doryphoros”; Policletus, the 5PPthPP cent. Demosthenes; Polyeuktos of Athens, the BC Roman marble copy of the lost 3PPrdPP cent. BC .........................................29 original made of bronze; National Venus of Milo, unknown artist, Louvre, Museum, Naples........................................ 57 Paris............................................................30 Constantine the Great; head of a destroyed Pharos lighthouse, Alexandria...........................30 gigantic statue, the
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