Fun with mathematics
SLICING PIZZAS, RACING TURTLES AND FURTHER ADVENTURES IN APPLIED MATHEMATICS: Robert B. Banks; Universities Press (India) Ltd., 3-5-819, Hyderguda, Hyderabad-500029. Rs. 350.
THE AUTHOR of the book under review, Robert B. Banks, has the background of four decades of experience in teaching and research at several universities in his home country, the U.S. and abroad.
His expertise has been availed of by the Ford Foundation in Mexico City and the Asian Institute of Technology in Bangkok.
Only a few mathematicians have shown interest in writing a book of general interest in applied mathematics.
Banks can be taken to have done an exceptionally good job with rare insight and initiative in this regard. His earlier published books Towing Icebergs, Falling Dominoes and Other Adventures in Applied Mathematics is a pacesetter.
Both the books are complementary. While in service, he has been collecting over years these themes and pondering over their popular presentation.
Realising the need for the educated to be alive to the increasing role of mathematics in the fast growing fields of science and technology, he makes a laudable enterprise in describing accurately and concisely numerous phenomena and situations experienced by everybody, as sources and venues of appreciating them as mathematical models.
The reader is, of course, expected to have competence in school algebra and geometry, differential and integral calculus, besides some grounding in analytical geometry and spherical trigonometry, statistics and probability required for understanding a few of the themes. Problems considered have roots in various disciplines including physical geography. As he himself observes, the book under review cannot be adopted as a textbook for the simple reason that it does not cater to any particular branch or syllabus.
There are always some students in junior and degree colleges whose curiosity transcends prescribed portions and the fare offered in the book will certainly whet their appetite for finding explanations of some of the commonplace issues that assail their questioning minds.
Non-availability of any source to seek or find answers leaves one dejected. This book not only provides relief and opening to get enlightened but an opportunity to take up similar topics for project work or contests in mathematics. The book, though weighty, is not bereft of humour and mirth in presentation and hence is enjoyable.
Chapter titles are tantalising and they are almost independent. They are worth brief mention: Slicing pizzas and water melons, Rain drops and volume of water, Rivers flowing uphill, Getting anywhere in almost forty two minutes, Running in the rain to get least wet, Turtle races, Number of people who have ever lived, Saving through mathematics in making Valentines and other greeting cards, Making mountains from mole hills, Flattening spheres and cartography, Moving continents, Problems of growth and its limit, Length of baseball seam and travels, Lengths, areas and volumes of all kinds of shapes and so on.
The author's love for mathematics is so pronounced that he finds himself writing with fervour three chapters seven, eight and nine differently from the rest. They cover the famous numbers <108,SYM,80>(pie the ratio of circumference to diameter), e (base of natural log), <108,SYM,102>(phi golden ratio), <108,SYM,103>(gama, Euler's constant, <108,SYM,100> (delta Feigenbaun number) that number mathematics landscape from ancient to modern times. Great number sequences Prime, Fibbonacci and Hailstorm, are also brilliantly treated.
The publisher would do well to bring out a separate booklet covering these chapters along for wider readership, the journalistic fraternity in particular.
The author makes a novel and welcome plea, which will be readily echoed; celebrate annually days marking some of them; <108,SYM,80>(<108,SYM,64>3.14) on March 14, e(<108,SYM,64>2.7) on Feb. 7, and <108,SYM,102> (<108,SYM,64>1.6) on Jan. 6.
Strangely enough though understandable, the book opens with a chapter on the U.S. flag and its geometry, a seriously undertaken mathematical exercise. This is followed by mathematically viewed slicing. One could say with envy that the author has developed his mathematical eye to the extent that he is able to take up non-routine matters for his delightful exposition.
While giving coverage, he gives in each chapter references to books for further study, besides a consolidated alphabetical list at the end and index. He has touched on fractal geometry as well though not fuzzy logic. The printing is error free. It would have been of great help to readers to have derivation of formulae given in an appendix.
The author has done a signal service in getting his refreshingly stimulating books published to serve as a corrective to the dull climate prevailing through stuffy examination-oriented teaching and learning of mathematics. Universities Press deserves thanks for publishing such books.
P. K. SRINIVASAN
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