On promoting Pythagoras’ Revenge in foreign lands

Last spring my husband and I went to the World Science Festival in Manhattan. He is a high school science teacher and I am the math editor for Princeton so we thought this was a great way to spend a Sunday afternoon. The exhibits were wonderful but our favorite was the Math Midway. It also was the most crowded. There were all kinds of hands-on exhibits, puzzles, and even a tricycle with square wheels. We loved the NASA exhibit and the Virginia Tech robot, Charlie, but we kept going back to the Math Midway. Seeing the excited, and sometimes concentrated, looks on the faces of kids and adults alike was almost as much fun as being a part of the action.

Even better than this, we learned that the Math Midway was a preview of what will become the Museum of Mathematics.  It will be a unique and innovative institution which will strive to enhance public understanding and perception of mathematics as an evolving, creative, and aesthetic human endeavor. Slated to open in Spring 2012, the Museum’s hands-on, interactive exhibits will provide a place for children and adults to become excited about math. MoMath will be North America’s only museum devoted to the wonders of mathematics and its many connections, from art to science to finance.

In addition to the exhibits that we saw in the Math Midway, there will be lectures, classroom events, and a gift shop where you can purchase all kinds of great math toys. If you just can’t wait, go to http://momath.org/shop to find a great math gift. You will also be supporting the Museum. If you would like to know more about the museum, visit http://momath.org/. If you will be attending the Joint Mathematics Meetings in New Orleans this January, please stop by their exhibit.

The story of this reprint began in the late 1980s. I was working at the Society for Industrial and Applied Mathematics and was getting quite a few requests to reprint the Ford & Fulkerson book on Flows in Networks in the Classics in Applied Mathematics series. This is a wonderful series that reprints books that are out of print. There was no Google at the time so finding the copyright holder was not as easy a task as it is today. The book was originally published in 1962 and had been out of print for quite a long time so finding a copy was also difficult. Due to many other duties, I pursued this off and on but did not have much time to devote to the search.

I moved to Princeton University Press in 2001 and was looking at the titles in the Princeton Landmarks in Mathematics series (also a series of classic books that had been published in another series or that had gone out of print) and thought again about the Ford & Fulkerson. It really bothered me that I had not followed through on finding the copyright holder. In 2004 I was visiting David Williamson at Cornell and he suggested putting the Ford & Fulkerson back in print. I started to tell him my long history with this book and he told me he didn’t think it would be a problem since Princeton University Press had published the book. Since the book was out of print, I had no record of it. What a wonderful surprise that was!

The next thing I had to do was actually find a copy of the book. Although this might sound ridiculous, we did not have one in our warehouse and there were no copies in the Princeton University library. I began to think it was just not meant for this book to be in print. Once again, I drifted away from the project. In 2008 I was back at Cornell and met Bob Bland who also suggested I put the Ford & Fulkerson back in print. I started to tell my long, sad story but he stopped me in mid-sentence and handed me a copy of the book. I had run out of excuses. We had a wonderful conversation and he told me that Fulkerson had been his advisor. Bob and James Orlin have written a wonderful new foreword which describes the continued importance of this book and its many applications, almost 50 years after it was originally published. If there are any other Princeton University Press books that you would like to see back in print, let us know.

Here, Princeton University Press author John Adam presents two math problems you might encounter in your quest for fall foliage this month. The problems and solutions are similar to those found in his books A Mathematical Nature Walk and draw upon the skills you described in Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin.

The season of Autumn can be one of great beauty, especially where the foliage changes to a bright variety of reds, oranges and yellows. Why do leaves change their colors in the fall? There are in fact several different reasons, but the most important is the increasing length of night and cooler temperatures at night. Other factors are the amount of rainfall and the overall weather patterns in the preceding months. Just like sunsets, the weather before each fall is different. Basically the production of chlorophyll slows and stops in the autumn months, causing the green color of the leaves to disappear, and the colors remaining are mixtures of brown, red, orange and yellow, depending on the types of tree. To have any real chance of seeing the wonderful fall foliage, you have to go to the right places at the right time. Going to the beach in summer or even the fall won’t do! And going to the Blue Ridge Mountains or New England in the depths of winter will not enable you to see the fall foliage either, pretty though the snow-covered trees may be!

But there are some other aspects of this season that are present at anytime of the year, and do not depend on the leaves changing. Those aspects involve trees, rain and, in this case, my left foot!

Consider this: you are in the hills of New Hampshire, or West Virginia, or perhaps you are somewhere on the Appalachian Trail enjoying the glorious fall colors, when suddenly a rain squall appears out of nowhere, or so it seems. You run to take cover in a deserted shelter a hundred yards away near the trail. Playfully (there being nothing else to do) you stick your foot outside the shelter, and of all things, photograph the rain falling around it! After ten minutes of intense rainfall, it stops as suddenly as it started. You wonder how fast that rain must have been falling to create the scene you now survey: large puddles all along the trail, drops dripping from every available leaf above you, and the temporary dark-brown stains on the trunks of rain-soaked silver birches.

As you set out on your way again, you start to notice the wave patterns formed when the drops falling from the branches above you hit the surface of puddles. Question: which of the following patterns represents this situation?

Answer: the one on the left. Raindrops falling on the surface of a puddle generate wave patterns that are dominated by the effects of surface tension. The speed of these waves is inversely proportional to the square root of the wavelength; thus shorter waves travel faster and move out first. Note the expanding region of calm associated with, and inside these waves. The other pattern is dominated by gravity, which produces longer waves with speeds directly proportional to the square root of the wavelength, so the longer waves travel faster and move out first.

Once home, you upload your pictures onto the computer. On noticing the picture you took back at the shelter, you realize that knowing the exposure time of the shot, you can estimate the speed of the rain. Here is the picture: can you find the speed of the rain?

This rather pedestrian photograph was taken from a sheltered area outside the Mt. Washington Resort, Bretton Woods, NH on September 30th, courtesy of Tropical Storm Nicole. Because of the heavy rain, Mt. Washington was nowhere to be seen! Nevertheless, it seemed like fun to “guesstimate” the speed of the raindrops, given that the exposure time for the shot was 1/200 second and an estimate of the width of my sneaker (you don’t need to know my shoe size to do this.). My foot and the raindrops shown were about the same distance from the camera. You can assume that the foreshortening of the rain streaks (due to the downward angle of the camera) is not significant.
Answer: From the photograph, The width of my sneaker is approximately 5 inches, so the raindrops travelled approximately 5/3 inches in 1/200th of a second, or 1000/3 inches/s, or 1000/36 ft/s. Therefore

Since 1 m/s 2.2 mph, this is about 8.6 m/s.]
For those who don’t have access to my foot, anything in the range 4 inches to 6 inches wide is a reasonable estimate. This would result in a range of speeds 15-23 mph (7-10 m/s).

“Have you ever taken a moment to thank a teacher or someone else who has helped you become what you are today? I haven’t, but I really wish I could,” says mathematics editor Vickie Kearn.

I had an amazing high school math teacher. Because I was at a small boarding school, I had the same teacher for three years. Elsie Nunn was about 4’5” tall, with Einstein-like hair. She was a whirling dervish and taught me an amazing amount of math using a broomstick, chalk, and a coat hangar. Because of Ms. Nunn, I knew I would major in math and be a school teacher. I did exactly that and taught math for eight years before entering the world of publishing.

In November 2006 Steve Strogatz called me and asked if I would be interested in publishing his new book about his thirty-year correspondence with his high school math teacher, Don Joffray. He told me that the focus of the book was on math problems they discussed through the mail and he also planned to show how their relationship matured and changed through the years. That sounded wonderful and my immediate answer was, “Yes!”. Steve told me that a trade house was interested but only if he would take out the math. That seemed ridiculous to me and I said we would want the book only if the math stayed in. Princeton was a perfect match and we began to work on developing the manuscript right away. Steve had an incomplete set of correspondence because he had not saved all the letters from his teacher and there were large gaps when he did not respond to Joff’s letters. (You will have to read the book to learn why.) The big task was how to write a story around the letters so that everyone would enjoy it—not just mathematicians.

We talked about the book and how it should be developed for a long time. The letters were all about math, which Steve would have to explain to some readers. It was also important to explain what was not in the letters—the non-math things happening in Steve’s and Joff’s lives. Some were quite personal and we had to decide which to include. Joff illustrated his letters with drawings of birds and fish and we knew we had to add them in some way. There were a few false starts, but nothing we tried was just quite right. One day Steve called me and said, “I know how to do it.” He sent me a sample chapter and I agreed that his plan would work. Although we stayed in touch, I didn’t see anything further for a while. A few months later, I got a package from Steve. I decided to take a quick peak while I ate lunch. It is rare that an editor gets the chance to read a manuscript from beginning to end in one sitting, but that is exactly what I did. I could not stop reading until I got to the last page. I had seen sample letters but reading them all together within the context of the story that Steve had told was amazing. I saw a teacher become a student and a student become a teacher. I saw a self-centered young man become a compassionate teacher, husband, and father. I understood why Joff lived through and for his students and why he was so thrilled by their accomplishments. The bond of the love of math brought Steve and Joff together and no matter what was happening in their lives, the math was constant. But, there came a time when it wasn’t quite enough and that is when you discover than a stronger connection had probably been there for a long time but neither of them realized it.

I did eventually finish my lunch but my napkin was tear-soaked. I had never read a manuscript that had such a strong impact on me. I have tried to find my math teacher but have not been successful. I fear that I will not be able to thank her for instilling such a love of math in me. Because of her, I have had a wonderful 30+ year career as a math editor.

Thank you Ms. Nunn, and thank you Steve.

More recently, Steve Strogatz wrote a popular weekly column for the New York Times Opinionator blog that was in essence a light, interesting introduction to big math ideas.