The Infinite in the Finite

The Infinite in the Finite

The Infinite in the Finite

The Infinite in the Finite


This book is an extended history of mathematics that places mathematical development firmly in its historical context. Each section begins with a description of the geography and history of the country considered. From there, lively retelling of the creation myths and legends leads on to a description of how its people wrote and counted. This is followed by relevant mathematical material. The book covers; * The geometry of stone circles in Europe * The area of triangles and volume of pyramids that concerned the engineers of the Pharoahs * The Babylonian sexagesimal number system and our present measures of space and time which grew out of it * The use of the abacus and remainder theory in China * Greek mathematics from Pythagoras to Pappus. Detailed accounts of the work of apollonius and Archimedes are given. * The invention of trigonometry by Arab mathematicians * The solution of quadratic equations by completing the square developed in India Each chapter has a mathematical case study which is discussed both in the context of thetimes and in th light of more recent developments. Worked examples are also included. "The author has woven together a broad historical backgrounding and some fairly detailed but accessible mathematics in amost exciting way." John Fauvel, author of Let Newton Be!


I have never read prefaces to books. As a student I came to believe that prefaces are the places where authors, relieved finally of the burden of their books, parade their stables of pet hobby-horses. the purpose of this preface is therefore not to bore the reader with my views on the teaching of elementary mathematics or its history. It is simply to tell a few stories about how I came to write this book, and to thank the people without whose help it would never have come into existence.

In the mid-1950s, I was very interested, like most children my age, in atomic bombs. Having read some of the popular accounts of the day, and seen some of the propaganda films of various 'ban-the-bomb' organizations, I was dissatisfied. I wanted to know how a nuclear weapon 'really' worked. I asked my cousin Michael, at the time manfully struggling through the Cambridge Mathematics Tripos. Michael told me that to understand how an atom bomb worked I would have to learn a lot of mathematics. After attempting unsuccessfully to teach me calculus, he suggested I started with trigonometry. He gave me E. T. Bell Men of mathematics to read. I loved the stories of the great mathematicians, but found I couldn't learn any mathematics from this book.

When I returned to school (Bedales) I went to the library to find a book on trigonometry. Being very small for my age, I remember how huge the library doors seemed. I emerged from the Bedales library with no knowledge of trigonometry, but clutching one fact which I have never forgotten; a radian is 57°17′44.8″. I had no idea why mathematicians should choose to measure angles in terms of this strange unit. Further trips to the library unearthed another book which I enjoyed; W. W. Sawyer Mathematicians delight.

By then my ideas on how I wanted to learn mathematics had begun to take concrete form. I wanted to learn mathematics as a story. Since no book that I could find presented the subject in this way, I rejected them all with the ferocity of childhood as 'a pack of trash'. I very quickly convinced myself that I was no good at mathematics. At the same time, however, I believed that behind the courses I sat through with rising irritation and incomprehension, there was a 'real' mathematics out of whose living force came the problems and solutions which seemed to me to appear at random.

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