Preface

In large measure, this book is a sequel to an earlier volume entitled Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics. As in the previous work, this book is a collection of topics characterized by two main features: the topics are fairly easy to analyze using relatively simple mathematics and for the most part, they deal with phenomena, events, and things that we either run across in our everyday lives or can comprehend or visualize without much trouble.

Here are examples of a few of the topics we consider:

You need to go from here to there in a pouring rainstorm. To get least wet, should you walk slowly through the rain or run as fast as you possible can?

What blast-off velocity do you and your spacecraft need to entirely escape the earth's gravitational pull?

The colors of America's flag are, of course, red, white, and blue. Which of the three colors occupies the largest area of the flag and which color the smallest?

What is the length of the seam on a baseball or the groove on a tennis ball?

What is the surface area of the Washington Monument and what is its volume? How many golf balls could you put into an entirely empty Washington Monument?

Some of these questions sound trivial, perhaps even silly. Even so, they do depict settings or situations that are easy to visualize and understand. With the help of mathematics, it is not difficult to obtain the answers. As we shall see, the level of mathematics ranges from algebra and geometry to calculus. Several problems involve spherical trigonometry.

Throughout the book, topics involving various fields of knowledge are investigated. For example, quite a few problems featuring geography and demography are examined. In other chapters, a number of topics concerned with hydrology, geomorphology, and cartography are analyzed. In addition, where it is appropriate and feasible, features are described that relate to the historical aspects of a particular topic.

For over four decades, I was engaged in teaching and research at several universities and institutes in the United States and abroad (England, Mexico, Thailand, the Netherlands). I collected most of the topics presented in the book during that period. My primary interests, as a professor of engineering, were in the fields of fluid mechanics and solid mechanics (statics, dynamics, mechanics of materials).

Although this book deals with mathematics, it is certainly not intended to be a textbook. It might, however, be a worthwhile supplement to a text at the high school and university undergraduate levels.

As was the case in my earlier book, my strong hope is that this collection of mathematical stories will be interesting and helpful to people who long ago completed their formal studies. I truly believe that many of these “postgraduate students” sincerely want to strengthen their levels of understanding of mathematics. I think that this is especially true as all of us enter a new century that assuredly will place heavy emphasis on mathematics, science, and technology.

Here are some more examples of topics we examine in the book.

A prime number is a number that can be divided only by one and by itself. Some examples are 1, 2, 3, 5, 7, 11, 13, 17, and so on. As you might want to confirm, there are 168 prime numbers less than 1,000. Can you guess the magnitude of the largest prime number known at the present time (1999)?

A beautiful Nautilus sea shell has a shape called a logarithmic spiral. This attractive curve is mathematically related to the well-known Fibonacci sequence and the ubiquitous golden number,

The most famous “numbers” in all of mathematics are π (the ratio of the circumference of a circle and its diameter) and e (the base of natural logarithms). It is interesting that these two important numbers are related by the equation e^iπ = –1 where The numerical values of π and e (to five decimal places) are π = 3.14159 and e = 2.71828. Would you believe that at the present time (1999), π has been calculated to more than 51 billion decimal places?

The number of people in the world is approximately 6.0 billion as we begin the new century. Is this a large percentage or a small percentage of the number of people who have ever lived on earth?

Most of the ice in the world is in Antarctica and Greenland. If all this ice melted, the oceans would rise by 75 meters (246 feet). What would this increase in water level do to Florida, Washington, D.C., the Mississippi River, and Niagara Falls?

Finally, I hope you will enjoy going through the book. In attempts to make things a bit easier, I have tried to be somewhat light-hearted here and there. We all know that mathematics is a serious subject. However, this does not mean we cannot be a little frivolous now and then.