on November 25, 2008
Suppose you are given a problem which says: "Three dogs are placed at the vertices of an equilateral triangle; they run one after the other. What is the curve described by each of them?" How would you solve the problem? If this makes you scratch your head a little, don't worry. This problem actually appeared on the Cambridge University Mathematical Tripos Examination in 1871 and is one of the so-called "n-bug" problem. Obviously when n goes to infinity, the curve of each bug becomes a circle. On p. 110, Professor Nahin started to analyze this problem by writing down the radial and transverse components of the velocity, and step-by-step, he showed us how to solve this seemingly complicated problem, yet only elementary calculus (and perhaps some college physics) is needed. The approach is elegant. This book, which has a subtitle of The Mathematics of Pursuit and Evasion, obviously has a lot of mathematics and many equations, and it is not for general readers who are afraid of math. However, the book provides many elegant pursuit problems with military applications. For those who enjoy the real applications of calculus and perhaps like do some calculations on the back of an envelope, this is a superb book.
on April 1, 2014
Pursuit theory has been a favorite mathematical recreation of mine since the early 1990's. In this book, the author explores many continuous and discrete pursuit/evasion situations with clarity and succinctness. I encourage anyone with a background in differential equations to work through the problems in this book. They are rewarding and may very well inspire new discoveries on the subject.
For the lay person, the problems are intriguing in their own right (e.g., "Pursuit of Invisible Targets") but the solutions are derived and expressed mathematically. At the very least, this book presents a truly fascinating application of mathematics to anyone who picks it up.
on May 11, 2009
This is an excellent review of the math of pursuit and escape paths. I have not read the book completely, but I concentrated my reading on a couple of problems I was mostly interested in: The Lady in the Lake problem, and the Lion-and-Man problem. These two problems are strictly connected, and have more immediate geometric explanations than the equations of the problems presented in the book. However, these alternative explanations are missing in the book; too bad because they add a lot to the understanding and intuition of the problems. In one case actually, (Lion-and-Man problem), I believe the outcome of the problem is different from the one provided. This doesn't detract from this enjoyable book, which is well written, with very approachable, step-by-step math passages.
on June 21, 2014
Whenever you see a Paul Nahin’s book, you may expect something nice, well-written about a theme in mathematics. With an undeniable ability to transform technical subjects into tasty and readable texts (for the layman), this partucular book is a treat for those interested in graph theory. Can’t miss it!