Showing papers in "The Mathematical Gazette in 1992"

The man who knew infinity by Robert Kanigel. Pp 438. £16·95. 1991. ISBN 0-356-20330-1 (Scribners)

Abstract: On a flight to Kansas this week, where I was participating in a scholarly communications symposium, I watched The Man Who Knew Infinity [2016]; a dramatisation of the life of the Indian mathematician Srinivasa Ramanujan as he travels to Cambridge and is eventually made a fellow of the Royal Society. I had previously encountered Ramanujan's extraordinary story when I had seen A Disappearing Number, a devised dramatic piece by Théâtre de Complicité and it has stuck with me ever since.

The Unexpected Hanging and other mathematical diversions , by Martin Gardner. Pp 264. £8.75. 1991. ISBN 0-226-28256-2. (University of Chicago Press).

Abstract: A magnetic recording element suitable for use in an automatic ticket vending unit and an automatic ticket checking and collecting unit which comprises a substrate and a layer coated thereon, said coating layer comprising 100 parts, by weight, of gamma -ferrite particles, 1 to 2 parts of a dispersing agent for gamma -ferrite, 5 to 15 parts of an alkaline modified protein, 15 to 30 parts of a rubber-like synthetic polymer and 1 to 2 parts of a hardening agent for protein is disclosed.

Nonlinear ordinary differential equations and their applications , by P.L. Sachdev. Pp. 578.$132. 1991. ISBN 0-82 47-836 4-6. (Marcel Dekker).

Abstract: Presents simple analytic methods which are readily accessible for use in applications. These include transformations, phase plane analysis, integral equation formulation, shooting arguments, local and asymptotic analysis, singular point analysis, and others. The applications, reflecting the research

Problems to sharpen the young

Abstract: An annotated translation of Propositiones ad acuendos juvenes, the oldest mathematical problem collection in Latin, attributed to Alcuin of York In researching the history of recreational mathematics, one finds that the Propositiones ad acuendos juvenes of Alcuin of York is frequently cited as the earliest problem collection in Latin. The text contains 56 problems, including 7 major types of problem which appear for the first time, and 2 major types which appear for me first time in the West. By any standard such a collection is of major historical interest, so it is surprising that a critical edition was not prepared until Folkerts' edition of 1978, and yet more surprising that no English translation has ever been produced.

Fractals, chaos, power laws ; Minutes from an infinite paradise, by Manfred Schroeder. Pp 429. £24.49. 1991. ISBN 0-7167-2136-8 (Freeman)

Abstract: Self-similarity is a profound concept that shapes many of the laws governing nature and underlying human thought. It is a property of widespread scientific importance and is at the centre of much of the recent work in chao fractals, and other areas of current research and popular interest. Self-similarity is related to symmetry analysis is an attribute of many physical laws: particle physics and those governing Newton's laws of gravitation. Symmetry, found throughout the biological universe, is also a basic property of the mathematical universe. In this book the author explores the idea's of scaling, self-similarity, chaos. and fractals as they appear throughout the universe of pure and applied mathematics. Because of his formidable research experience, stretching from the acoustical modelling of concert halls to pure number theory, Schroeder is able to take the reader on an intellectual excursion through this vast forest of topics. Requires a basic familiarity with undergraduate mathematics and elementary physics.

Laplace transforms and an introduction to distributions, by P.B. Guest, pp411. £40 hbk, £19.99 pbk, 1991, ISBN 0-13-523549-9 hbk, 0-13-524810-8 pbk (Ellis Horwood)

Abstract: This multi-purpose book introduces graduates and advanced undergraduates in mathematics and the applied sciences to a rigorous treatment of the Laplace transform and the theory of distributions (or generalized functions) - two important areas of modern pure, and applied, mathematics.

Why Teach History of Mathematics

Abstract: There are questions which have only personal answers. One such question is the one in the title; another, which is intricately bound up with it, is: Why teach mathematics? On the following pages you will find my personal answers to both questions; a selection of other people's answers to one or both are listed at the end. Much longer lists could be made, and very long ones if one included also papers in other languages than English. As you will see, my list contains papers from different parts of the world and from different times in this century; it seems that many people agree, for different reasons, that one really should teach history of mathematics, but that it has to be said again and again.

The remarkable Ibn al-Haytham

Abstract: ‘I saw that I can reach the truth only through concepts whose matter are sensible things and whose form is rational.’ The achievements in experimental and theoretical science of the Arab scholar al-Haytham (also known as Alhazen, from his latinized first name al-Hasan) make him as much a figure of the sixteenth and seventeenth centuries as of his own tenth and eleventh centuries. When his writings become known in the West the importance of his contribution to optics was widely recognized and he was studied by Galileo, Kepler, Fermat, Snell and Descartes. Mathematicians remember al-Haytham chiefly for Alhazen's Problem on the reflection of light from a circular mirror, which he solved by the method of conic sections; Huygens, Gregory, l'Hospital, Barrow (and many others) later took up the problem with the new analytical methods of geometry. Al-Haytham also wrote a commentary on the postulates of Euclid, and his attempted proof of the parallel postulate has similarities to Lambert's quadrilateral and Playfair's axiom in the eighteenth century. His theory of cognition may produce yet further interest in his work.

Seventeenth century instruments for drawing conic sections

Abstract: One of the consequences of Descartes’ new approach to geometry (1637) was an increased interest in instruments for drawing conic sections. Conic section drawers, which is the name I shall give to instruments for drawing conic sections in a continuous movement, had been described earlier, but the central role of conic sections in the geometry of Descartes made them by about 1640 into a new topic of research. This article sketches the background to this growing interest and then describes some of the instruments designed by the Dutch mathematician Van Schooten (1615/6 – 1660). It concludes with an application of this material in mathematics teaching.

Minimum wage policy

Abstract: Before the last General Election politicians were arguing about the effects of a minimum wage policy. One was suggesting that we should have a minimum wage that was a certain percentage of the mean wage, while another claimed that such a policy would be inflationary, with wages spiralling up like a dog chasing its tail. What struck me was if you give some people an increase in salary to a fraction of the mean salary then you’ve increased the mean, so you’ll have to do it again. Might this process not lead to wages spiralling up to infinity?

Archimedes’ revenge: the joys and perils of mathematics , by Paul Hoffman. Pp 285. £6.99. 1991. ISBN 0-14-012506-X (Penguin)

Abstract: A collection of articles on the highways and byways of mathematics. The book is written in the tradition of Martin Gardner and aims to be both entertaining and fascinating.

Word problems and equations: an historical activity for the algebra classroom

Abstract: The following activity is one of a series developed for junior high school students (age 12-15). Each of the activities involves a historical discussion of a subject related to a certain curriculum topic, and takes the form of a teacher directed presentation/discussion with accompanying transparencies and worksheet. The choice and development of the activities was guided by certain general principles. The connection between the regular curriculum and the selected subject is meant to give relevance to the history and also, to motivate and deepen student understanding of subject matter. The structure of the activity enables the teacher to change, omit, or to add if he wishes. Points for discussion and questions to be worked are deliberately inserted at intervals to activate students, because in previous trial versions which were closer to the lecture format we found that students lost the thread and hence, also interest. Reactions to the present format were much more encouraging.

Historical stories in the mathematics classroom

Abstract: Some years ago when I was co-editor of the German periodical Mathematik lehren we decided to prepare an issue on the history of mathematics. To secure the interest of our usual readership, we planned to elaborate a few hints, recommendations, or suggestions on how to include historical items in the ordinary teaching of mathematics in school. It soon became clear however that this methodological problem would be the critical point of our project. It turned out, as I had feared from the beginning, that only a very few of my colleagues could be talked into writing about this feature of the subject. It was easy to get papers on historical facts or on hypothetical developments, but everyone found it hard to write about practical ways of teaching history in the mathematics classroom.

Newton's teaser

Abstract: This article looks at some of the history of “Leibniz's series” and at Newton's riposte in a letter to Leibniz, the Epistola Posterior : On the way we shall take in Gregory's well known contribution to the problem, and Newton's own description of how he discovered the binomial theorem using a method that has considerable appeal in classrooms today. For light relief Newton's apples will make an entrance. I have tried to track down as many copies of the original manuscripts as possible, as these have a great motivating effect on students. Knowledgeable readers will realise that this article is really an extended review of three magnificent sources, The Mathematical Papers of Isaac Newton , edited by D.T. Whiteside, Leibniz in Paris 1672-1676 , by J.E. Hofmann, and The Correspondence of Isaac Newton edited by H.W. Turnbull. My interest in the history of mathematics stems from a conversation with Professor Whiteside at the MA conference at Leicester in 1990, during which it became clear to me that despite having read and digested the works of Bell, Kline and Boyer, I knew nothing of the history of the calculus I was supposed to be teaching.

Teaching geometry to 11 year old “medieval lawyers”

Abstract: In 1355 the Italian professor of law Bartolus of Saxoferrato (1313-1357) wrote a treatise on the division of alluvial deposit. The problem he discussed is the following (figure 1). Some landowners, Bartolus calls them Gaius, Lucius, and Ticius, have neighbouring properties beside the bank of a river. The river deposits silt so that new land is formed at the riverside. How is this new fertile soil to be divided up ?

Who named the radian

Abstract: While looking at old copies of the journal Nature I chanced upon correspondence regarding the origin of the word radian. Textbooks today simply state it is an angular measure and have no interest in, nor space for, the history of the word. The Oxford English Dictionary states that the word first appears in print in 1879 in the second edition of the Treatise on natural philosophy by William Thomson (later Lord Kelvin) and Peter Guthrie Tait. In their discussion of angular velocity they wrote: “the usual unit angle is … that which subtends at the centre of a circle an arc whose length is equal to the radius. For brevity we shall call this angle a radian.”