© ATM 2010 • No reproduction (including Internet) except for legitimate academic purposes • [email protected] for permissions. Sixth Form College. Just looking at in whichy is the elevation of the water what was in everyday use not so long surface above or below the average ago gives some amusement. Did you level, x is distance, t is time and C is know that one slug was 14,606 the velocity of the waves'. The analysis kilograms? (I know that those in my carries on from there. garden are rather smaller). Or that the Although the author's back­ density of air is 0.00233 slugs per ground is in mechanics and fluid cubic foot? Rather more worrying is dynamics, the examples given in the the fact that a respected academic in book range far more widely, from the States does not recognise that population statistics to geography and things have changed this side of the economics. Some chapters take a Atlantic. single theoretical background with a ADVENTURESWITH This aside, the book takes a variety of applications. Thus, falling number of everyday and more dominoes are linked to tidal surges MATHEMATICS unusual situations and explores them. and wave motion. Ann Kitchen What happens and why does it The format of each chapter is the happen? How can the theory be used same. So chapter 14 deals with in other related situations? His style is skipping ropes and wind turbines. light and in places perhaps he over­ Now, to you and I there might not be Towing icebergs. falling simplifies, but those willing to read much connection between the two, dominoes and other adventures with care will find a wealth of starting but Professor Banks takes us through in applied mathematics points suggested. the mathematics of pendulums, Robert B Banks The book starts with a descrip­ ellipses and elliptic integrals to the tion of the enormous meteorite that mathematics of the Troposkein, or to Professor Banks has been involved in hit Arizona over 20,000 years ago. the less initiated, the shape a skipping teaching and research in engineering This is used as a focus for explaining rope makes when in use. This leads over the past forty years. He looks on the term Mach number: how, in any smoothly to the Darrius wind mathematics as a beautiful and given medium, it is given by the ratio turbine, whose blade is designed to be intriguing language that can describe, of the speed of the body to the speed the same shape. The book is not accurately and concisely, the almost of sound in that medium. This leads designed to be read straight through. limitless list of phenomena that we seamlessly to the calculation of the Find a chapter that interests you see all around us. His joy and delight speed of sound in both air and water. particularly and read it. in these is evident to all who read the As a teacher I might well want to look So why buy and read the book? It book. His stated audience is mainly more deeply into this phenomenon. is a must for any school library. The those who have finished their formal How does the speed of sound vary as diversity of topics and the easy style education in mathematics. However, the density of the medium decreases? mean that it may well be the way to his book is equally accessible to those What affects the distance sound introduce students to modelling and who are still learning or using mathe­ travels in any medium? Answers to to the importance of modelling to matics. It is not a text book, more a questions such as these are not to be almost every field of human book of exploration of ideas and found. Professor Banks passes lightly endeavour. Equally, it may provide concepts linked together by mathe­ on. And yet, perhaps this is a good the germ of an idea for a new investi­ matical modelling. thing. It would be all too easy to go gation or a way that a well known What is the place of this book in deeper and deeper into the mathe­ investigation may be extended or teaching today? Firstly, it is not a matics until all but the most gifted altered. There are some suggestions book that one can pick up and use to mathematician had become lost. This for such projects but no detailed teach. Those who are looking for a set has not happened. Instead, the work answers. Those will be for the reader of finely worked out solutions to an both helps the reader to get a feeling to provide. However, there is a equally well-defined set of problems for the model and work out a simple comprehensive set of references to will be disappointed. But those who solution, and also gives ideas to those books and articles that may well give want to get ideas for explorations of who have the ability, knowledge and you the answers you need. their own, to find methods of contin­ inclination to go further. The purist, All in all, this is a book that is well uing and refining the models given or however, could rightly point out cases worth having. to enjoy looking at and trying to where the mathematics was too follow mathematics just beyond their simplistic. Certainly there is no TO'Wing icebergs,jalling dominoes own level of attainment will find a and other adventures in applied attempt to provide step-by-step wealth of material here. This is not to mathematics. Robert B. Banks, 1998, proof. So, when investigating waves in say that there are not some anomalies. Princeton University Press.ISBN 0-691- water, the analysis starts with the The author writes for the US market 05948-9, 328pp. £19.95. words 'We could analyse this problem and those studying in Britain will be by using the equations for the conser­ hard put to recognise the set of units Mechanics in Action Project, vation of mass and the conservation that he states as being in common University of Manchester of momentum. Doing so we would everyday use in Britain. Poundals and obtain the following equation: slugs have long since disappeared from the vocabulary of the average df 60 MTI68 SEPTEMBER 1999 Academic copyright permission does NOT extend to publishing on Internet or similar system. Provide link ONLY © ATM 2010 • No reproduction (including Internet) except for legitimate academic purposes • [email protected] for permissions. reminder of much mathematics I had There are several reasons: ANOTHER LOOK AT forgotten I ever knew and gaining • because at its heart it is a series of THE LAST THEOREM new insights into things learned long papers about one teacher's class­ ago. The ten appendices range from a room; Jenny Murray proof of Pythagoras' theorem to an • because there is not enough example of proof by induction. You do known about what forms of talk not have to read them, but you best promote mathematical probably will want to. understanding, nor the processes Fermat's last theorem The human side of the story by which this is achieved; Simon Singh comes through particularly at the • because it is published in a series like many others, I want the books I end, when the flaw was found in the about situated learning and read to be both entertaining and of proof. The penultimate chapter reads cognition, and I wanted an more than passing interest. I like a more like a detective story or thriller, opportunity to grasp these ideas book which falls in the mean between as Andrew Wiles worked towards the for MT; 'once picked up, you can't put it final breakthrough. Perhaps this is a • because it raises some interesting down' and 'once put down, you can't point at which you would be unwilling questions about the relationship pick it up'. Fermat'slast theorem is to put the book down. between research and practice. just such a book: eminently readable, But this is only the penultimate but in no way tyrannical. It has chapter. So many amateur mathe­ One teacher's classroom enough of the human story to keep maticians have worked on Fermat's Magdalene Lampert taught in a the non-mathematician happy and last theorem. What could they do variety of different schools for twenty interested, and enough mathematics now? The last chapter gives many years before she moved into research. to have an erstwhile number theorist unsolved mathematical problems Towards the end of her teaching like me engaged in a delightful which, like Fermat's last theorem, are career she created video, audio and version of a revision course. Of easy to understand with a knowledge written records of her teaching with course, as the story unfolds, as the of elementary mathematics. Lots to one class for a whole year, realising mathematics develops, nearly all get those talented sixth-formers that they would be a rich resource for readers will join the ranks of the non­ working away on! future investigations. Four chapters of mathematicians (those who do not this book are based on analysis of her really know exactly what is going on), Fermat'slast theorem, Simon Singh, practice. There is no intention to say 1998, London: FourthEstate, ISBN 1- because the proof covers areas which 'this is an excellent teacher and we 85702 -669-1, 362pp, £6.99 'only half a dozen people in the world should all be copying her'; rather the could fully grasp'. Suffolk idea is to use her practice to highlight There are three threads twined some of the things that teachers do, together in the book.