Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics (Princeton Paperbacks)

Rating:
Summary: A truly excellent book on applied mathematics
Review: Don't be misled by the title; this book is not for everyone. Unless you are very comfortable with calculus and have more than a nodding acquaintance with differential equations this book isn't for you. The author does a good job of providing solutions to interesting problems through applied mathematics. However, he does something that mathematics professors always did that used to drive me crazy and it still does. He sets up a model, develops some defining equations and then makes a leap with something like "using these relationships, it can be established that ..." or "With this information, we easily determine that ..." Some intermediate steps would have been helpful.

The book is interesting and entertaining but without a background in calculus and an understanding of ordinary differential equations, you won't like it.

Rating:
Summary: Great, unusual problems solved in detail
Review: The charm and attraction of most of the problems in this book comes from their unusual nature. I for one probably would have never thought to ask what the relative areas of the colors are in the flag of the United States. Another fascinating computation deals with how many times the world's water has been consumed (ingested) by humans. Not surprisingly, it is on the order of one part per million. An interesting supplemental problem would be the rate of change of this ratio. Given the high current population, the rate of increase is the highest in history. While the problems are extremely interesting, one is often hard pressed to find a practical application for the results.
My favorite problem is the computation of the length of the seam of a baseball. The problem fits in well with the mindset of baseball aficionados, who adore obscure statistics concerning the sport they love so passionately. When the weather turns bad, there is not one person among us who has not stood in a shelter and asked the question, "Will I get more rain on me if I run as fast as I can or if I just walk?" The answer here is thorough, as the author even considers the amount of water that splashes on you when your feet hit the ground. To learn the answer to this pressing question, you will have to read it for yourself.
If you ever wish to complete my childhood fantasy of going to China by the direct route through the Earth, then you will want to read chapter 11 before you make the attempt. Assuming you can iron out all the minor engineering details concerning the molten core of the Earth, you will need to understand what will happen to an object at one end of the shaft if it is dropped. The journey to the other side of the Earth would also be a surprisingly short one, roughly forty two minutes in duration.
Learning and teaching mathematics requires that certain problems be presented and solved. However, once the core is covered, consider taking a sideways trip and explore these delightful oddities. It is well worth the effort.

Rating:
Summary: A truly excellent book on applied mathematics
Review: This book, together with the author's earlier title "Towing Icebergs, Falling Dominoes" belong to the bookshelf of everyone who loves applied mathematics. They contain some of the best examples I have ever seen on "applied" math (versus many other great titles on "pure" math), represented by numerous fun and funny cases. Read the preface and be intrigued by the questions addressed in them. As all good scientists and engineers know, the key to problem solving is really not math, but how to apply them, how to "model" or "approximate" real world cases. That's what these 2 books are all about.

To fully appreciate these problem-solving skills, you need to be comfortable with advanced calculus or basic differential equations (probably at the halfway point of these courses). On the other hand, students who are taking these courses should read Banks' books just to see what they are really learning. Math really comes to alive through these pages. I had a great time.

Rating:
Summary: Readable applied math.
Review: This is a fine compendium of math applied to a variety of real world problems. The only thing that bothers me is, where are the problems for the reader to try on his own?!

I mean, a lot of people who are going to read this type of book like the challenge of solving a few problems on their own. The author provides scanty few problems to solve, but geez, even for those he doesn't provide the solutions?! - to me this is a cardinal sin when it comes to expository math books -sorry. So please, next time include a few problems for the reader "a la Martin Gardner"

But it is otherwise a very fine book full of spoilers for us math puzzle freaks.

Rating:
Summary: Great math reading
Review: This is a great book if you like college level applied mathematics. There is a great array of different types of problems that uses algebra, trigonometry, calculus, statistics, and differential equations.

Rating:
Summary: Fun with math.
Review: This is one of the most delightful books I've read in a long time. I have one other book by Banks, "Towing Icebergs, Falling Dominoes, and other adventures in applied mathematics." Like "Towing Icebergs," "Slicing Pizzas" is jam packed with sometimes useful, sometimes trivial, but always entertaining mathematical excursions into some of the most interesting little "didja know?" subjects in applied mathematics. If you have inquisitive kids - or if you are one yourself -- it's a definite must read.

The book is a little over 250 pages long, and there are 26 chapters, so each chapter is pretty brief - typically only about ten pages. Most of the mathematics in the book is algebra, trigonometry, geometry, and a little bit of calculus, and the book is literally packed with mathematical equations and diagrams. Just because most of the mathematics is at the high-school level, however, does not mean that it's necessarily easy or trivial. When it comes to "mess'n with math" Banks is a real pro, and I found myself on more than one occasion taking up to 30 minutes filling in the details from one of his equations to the next.

What's fun about Bank's book is that it goes after problems you might not have thought about. And when Banks starts going into detail it can really make your head spin. Take, for example, the American flag. How much could you write about the mathematical description of the flag? Well, Banks packs more information than you might suspect into 22 pages (chapter 1 and lots of chapter 2). It seems that just about everything you can say about the flag (mathematically speaking) and about five-pointed stars and golden ratios is tied up in this chapter. Ever wonder what percentage of the flag is blue, white, and red? Banks will tell you.

Caroline particularly got a kick out of chapter 3. She is 10 years old and loves pizza, so when Banks decided to write a chapter on how to cut a pizza to get the most number of pieces for a given number of cuts she could relate. Think it's easy? Try working the problem and then compare your answer with Banks. When you are done, do it for watermelons (that is, do it in three dimensions).

Have you ever wondered what is the best strategy in getting from one point to the next through a rainstorm? Is it best to run fast and minimize the amount of water on your head whilst soaking your front and splashing your feet and legs? Or, should your run a little slower, get a little wetter on top, but keep your legs and shoes a little less damp? This is yet another example of the seemingly whimsical yet eminently practical and always mathematical problems that Banks entertains us with (chapter 4).

Then there are those tidbits for spouting out around the dinner table during awkward times when everyone stops talking. "Hey, guess how many times the oxygen in the world's atmosphere has been breathed by people" Or "Hey, guess how many times the water in the world has been drunk by people"

Now here is an interesting idea. Because the earth spins on its axis it is an oblate ellipsoid, which means that its diameter is greater at the equator than at the poles. Banks asks the question, "which rivers run up hill." That is, which rivers have their mouth further away from the earth's center than their heads? Think it isn't possible? Think again and then read chapter 6.

Many of the problems that Banks solves deal with spherical geometry and trigonometry. For example, how would you go about calculating the length of the seam on a baseball or tennis ball? Banks does it in chapter 24 in what is probably the most mathematically intense chapter. It's not as easy as you might think.

Chapter 9 is about great number sequences, and Banks finds a practical application in - among all things - the problem of how the captain of a destroyer would go about tracking down an enemy submarine. Who would have thought there was a connection? There are too many examples to mention them all, but rounding out my favorites are chapters on how to make a valentine, how to pursue prey, how many people have ever lived on earth, population explosions, and (my very favorite) what makes a rainbow.

This book is very much in the same flavor as Bank's other book, "Towing Icebergs." It also has much of the same flavor as James R. Newman's four-volume set "The World of Mathematics." If you are acquainted with any of those books, and found them interesting, I think you will like this one.

One of the things I like best about this book is the frequent use of homework assignments. In lots of cases Banks takes the reader through to the bitter end, but in others he leaves tantalizing tidbits for the really enthusiastic readers (though he often provides answers - something welcome, in my opinion). The only real complaint I have about the book is it's utterly useless index. This is such a fun book, and covers so much material that it's real shame you cannot go look up many of the topics it discusses by using the index. For example, some of the most interesting information in the book deals with the golden number and golden ratio, yet neither "golden number," or "golden ratio" is in the index. I read the book with a pen and marker, so I updated the index in several cases.

If you love mathematics and doing mental calethsentics I think you will really enjoy this book.