# Essays on the history of mechanicsby Antonio Becchi; Massimo Corradi; Federico Foce; Orietta Pedemonte

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Essays on the history of mechanics by Antonio Becchi; Massimo Corradi; Federico Foce;Orietta PedemonteReview by: MICHAEL DE VILLIERSThe Mathematical Gazette, Vol. 92, No. 523 (March 2008), pp. 180-181Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/27821755 .Accessed: 30/05/2014 17:05Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org. .The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access to TheMathematical Gazette.http://www.jstor.org This content downloaded from 108.74.17.117 on Fri, 30 May 2014 17:05:58 PMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/action/showPublisher?publisherCode=mathashttp://www.jstor.org/stable/27821755?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp180 THE MATHEMATICAL GAZETTE This is a translation of the book originally entitled Si Einstein m'?tait cont? published in 2005. It is another window on Einstein written in a very readable style. TONY CRILLY Middlesex Business School, The Burroughs, Hendon, London NW4 4BT e-mail: t.crilly@mdx.ac.uk Essays on the history of mechanics, (in memory of Clifford Truesdell and Edoardo Benvenuto), Antonio Becchi, Massimo Corradi, Federico Foce & Orietta Pedemonte, (edrs). Pp. 256. EUR 42.00 (hbk). 2003. ISBN 3 7643 1476 1 (Birkh?user Verlag). The history of mechanics applied to constructions in building and architecture is relatively recent. This book is dedicated in memory of Benvenuto (1940-1998) and Truesdell (1919-2000) who were two major figures in the development of this field in the past twenty to thirty years, and is based on a symposium held in their honour in Genoa in 2001. This book also forms part of an ongoing series by Birkh?user called 'Between mechanics and architecture'. In the first chapter Hey man (p. 10) writes that Truesdell as an applied mathematician was well aware of the contempt he was in danger of arousing when he first 'defected' from his 'proper' research work to study the history and development of mechanics. Sadly, it is often claimed that when inspiration for 'real' mathematical or scientific research runs dry, the scientist starts dwindling into becoming just 'a philosopher of science', implying that it carries a lower status. However, when one reads over the analyses of the historical works of major mathematicians and scientists such as Galileo, Bernoulli, Leibniz, Newton, and Euler, to name, but a few, one can only marvel at the major contributions they made to modern engineering, and architecture. For example, the tremendous challenge faced by Euler in 1744 with a hideous non-linear fourth order differential equation in modelling elasticity. Heyman (p. 18) points out that unfortunately in the past century there seems to have developed a divide between pure mathematics and applied mathematics such as engineering. For example, already in 1936 a Russian mathematician, Gvozdev, developed the fundamental theorems of the theory of plastic structures, whereas the engineering community carried on largely experimentally in their approach to plastic design. Not until the 1950s was a more rigorous structural theory for plastics developed, based on Gvozdev's work and the collaborative efforts of mathematicians, physicists and engineers. The book is spread over 10 more chapters discussing the works of a many number of scientists like Lagrange, Klein, Navier, Poisson, Beltrami, Michell, Mann, Hooke, Carnot, Laplace, Cauchy, Chasles, etc. It virtually reads like a Who's Who in science and mathematics. The main topics that are dealt with are deformation theory, mechanics of timbrel vaults, rose windows in churches, vectors, Newton's principles of motion, and impact theory. The chapter on timbrel vaults is nicely illustrated with photographs of timbrel domes under construction; and in other chapters original historical drawings by scientists or engineers are reproduced. Particularly interesting to me was the graphical methods used by many of the engineers, and also the reproduction of De la Hire's 1702 figure to show the parallelogram law of forces. Stevin in 1605 apparently was the first person to discover the parallelogram law of forces while studying the equilibrium of a thread loaded with some weights (also illustrated with a copy from the original). His further studies led to the analysis of the forces acting on a hanging chain or rope, i.e. the catenary. Notably, quite a lot of geometry was evident in much This content downloaded from 108.74.17.117 on Fri, 30 May 2014 17:05:58 PMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/page/info/about/policies/terms.jspREVIEWS 181 of this early work on mechanics extending to Daniel Bernoulli's and Huygen's further studies of the catenary, Newton's laws of motion, etc. The chapter by Caparrini dispels the misconception apparently portrayed in every book on the history of mathematics, that the birth of vector calculus was a direct consequence of the discovery of the geometrical interpretation of complex numbers by mathematicians such as Wessel, Argand, Gauss, and others in the period 1799 to 1831. Instead, the author argues and shows evidence that the roots of vector calculus can be traced further back to the sixteenth and seventeeth centuries (as alluded to by the work of Stevin and others), and even some of the ancient Greek authors. Moreover, he argues that the historical intepretation reflected in current books on the history of mathematics neglects to mention the fundamental influence that mechanics and geometry had on the development of the vector calculus. Basically, the scalar product arose from analytic geometry (the projection of line segments onto straight lines), while the vector product was the translation into the language of pure geometry the analytic expression for the moment of a force. Despite the common view that Newton discovered universal gravitation, and that since his time essentially no new principles to have been added Newtonian mechanics, this is also incorrect. In fact, it is argued in the chapter by Maltese (p. 203) Newton's Principia contains no equations for systems of more than two free mass-points, and gives no evidence of Newton having being able to set up differential equations of motion for more complex mechanical systems. Indeed, the common interpretation denies the major developments that Lagrange, Euler and Bernoulli, for example, made towards what is today known as 'Newtonian mechanics'. The last chapter is a philosophical reflection on the role and aim of studying the history of science. An obvious reason is that it enables deeper understanding of a scientist and his or her work. For example, Andr? Weil apparently once said in a private lecture: 'after having now penetrated into Euler's work on number theory, I think that I know him better than I know most of my best friends'. Perhaps the strongest case to be made is that it helps one to understand the origin of ideas and how theories developed, changed and matured over time. As the Dutch mathematician and educator Freudenthal was apt to say: it provides insight into how humans have learned over the ages, and by doing so, can also give us some useful insight into how children may learn the subject matter. However, an irritation of the book was that in several places quotes by mathematicians and scientists were given in the original language (e.g. French, Latin or Italian), but no English translation was provided alongside or as a footnote. The book will clearly be of general interest to mathematicians, engineers, and scientists with an interest in the history of science. MICHAEL DE VILLIERS University of KwaZulu-Natal, Edgewood Campus, Ashley 3605, South Africa Fibonacci numbers, by Nicolai N. Vorobiev. Pp. 176. EUR 28.97. 2002. ISBN 3 7643 6135 2. (Birkh?user Verlag). The Middle Ages really only produced one notable mathematical work, namely, Liber Abaci, by the Italian mathematician, Leonardo of Pisa, better known by his nickname Fibonacci. This famous book was first published in 1202 and again in 1228, and contained almost all the arithmetical and algebraic knowledge of those times. Apart from also making Europeans aware of the value of the Hindu-Arabic number system, Liber Abaci contained a problem about breeding rabbits, that led to the introduction of the famous Fibonacci numbers. This content downloaded from 108.74.17.117 on Fri, 30 May 2014 17:05:58 PMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/page/info/about/policies/terms.jspArticle Contentsp. 180p. 181Issue Table of ContentsThe Mathematical Gazette, Vol. 92, No. 523 (March 2008), pp. 1-192Front MatterNice polynomials with three roots [pp. 1-7]A geometric interpretation of equal sums of cubes [pp. 8-13]The Divine Proportion, matrices and Fibonacci numbers [pp. 14-21]The power of a point for some real algebraic curves [pp. 22-28]Twenty-one points on the nine-point circle [pp. 29-38]Euler's and Barker's equations: A geometric derivation of the time of flight along parabolic trajectories [pp. 39-49]A serendipitous path to a famous inequality [pp. 50-54]Computing Farey Series [pp. 55-62]Notes92.01 Of grand-aunts and Fibonacci [pp. 63-64]92.02 The number of S.P numbers is finite [pp. 64-65]92.03 A uniform construction of some infinite coprime sequences [pp. 66-70]92.04 Square-free integers once again [pp. 70-71]92.05 When is the sum of consecutive n th powers an n th power? [pp. 71-76]92.06 A relation between the roots of a polynomial and its coefficients [pp. 76-81]92.07 A generalised algebraic identity bites Pythagoras [pp. 82-83]92.08 Summing digits of an arithmetic sequence [pp. 83-86]92.09 Explicit polynomial expressions for sums of powers of an arithmetic progression [pp. 87-92]92.10 Evaluating $\sum_{n=1}^{N}(a+\mathit{nd})^{p}$ again [pp. 92-94]92.11 A remarkable formula [pp. 94-96]92.12 Two infinite nested radical constants [pp. 96-97]92.13 The -binomial inequality [pp. 97-99]92.14 Some aspects of the behaviour of the graph of f1 (x, y) f2 (x, y)... fN (x, y) = [pp. 99-105]92.15 An improved approximation to a well-known integral [pp. 106-110]92.16 Avoiding Pythagoras [pp. 110-111]92.17 Magic knight's tours for chess in three dimensions [pp. 111-115]92.18 Generalisations of the Napoleon theorems, and triangles circumscribing a given triangle [pp. 115-124]92.19 Orthologic triangles and Miquel's theorem [pp. 125-128]92.20 Application of inversion to touching hyperspheres [pp. 128-133]92.21 Area and perimeter ratios [pp. 133-134]92.22 Maths bite: averaging polygons [pp. 134-134]92.23 Tilings into tilings [pp. 135-137]92.24 Counting faces on Archimedean solids [pp. 137-137]92.25 Finding lost cousins [pp. 138-141]92.26 An elementary proof of the generalised Fermat problem [pp. 141-147]92.27 The number of HH's in a coin-tossing experiment and the Fibonacci sequence [pp. 147-150]92.28 Angles in croquet [pp. 150-153]92.29 Three scenarios involving elastic collisions [pp. 154-158]Teaching NotesThe distance from a point to a line [pp. 159-160]A rapid method to find a tangent to a circle [pp. 160-160]Integration without tears two for the price of one [pp. 160-162]A surprise with parallel lines: an exploration that went wrong, then right [pp. 162-164]Feedback [pp. 165-167]Correspondence [pp. 167-169]Problem Corner [pp. 170-175]Student Problems [pp. 176-178]ReviewsReview: untitled [pp. 179-180]Review: untitled [pp. 180-181]Review: untitled [pp. 181-183]Review: untitled [pp. 183-184]Review: untitled [pp. 184-186]Review: untitled [pp. 186-186]Review: untitled [pp. 186-187]Review: untitled [pp. 187-188]Review: untitled [pp. 188-190]Review: untitled [pp. 190-191]Back Matter

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