He applied the “Page 99 Test” to his new book, Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics, and reported the following:
Context is important, especially in mathematics. Our brains are overwhelmed each day with an excessive amount of data. Without motivation, abstract mathematics will be tossed out in our nightly purge with the rest of our useless short term memory. Context also helps us understand difficult concepts by giving us a model to supply meaning to abstract mathematical relations. Once we have a working paradigm, we can tie together disparate notions into the big ideas that define a subject. Count Like an Egyptian is a book on ancient Egyptian mathematics and page 99 is the beginning of a section that illustrates the importance of context.Learn more about Count Like an Egyptian at the Princeton University Press website.
The section starts by describing the annual flood of the Nile. It then explains how Egyptians knew it was coming, how high it would be and how they would trap the life bringing waters and fertile soil it carried. As the flood waters receded, ancient Egyptians confronted a new problem. The old boundaries that marked one farmer’s field from another were washed away. Even worse, the river may have changed its course making it impossible to reestablish the old borders. The best they could do was to give a farmer a new field of the same area.
Now that the importance of area has been established, the book describes various field area problems modeled after actual 3,600 year old word problems. It starts with rectangular fields. Since rivers rarely agree to cut fields at nice right angles, it then explains how Egyptians calculated the area of other shapes. As always the book then presents the reader with problems so they can directly experience ancient methods.
The section ends with the solution to one last problem. The answer is surprisingly short and elegant. It’s here one of the main themes of book is reexamined. Modern mathematics is dominated by equations and algorithms. If you follow the prescribed steps mindlessly you will obtain a correct answer. Ancient Egyptian mathematics favors creativity and wit. It provides a set of tools to be used on a whim. In the hands of the skilled, Egyptian math can reduce long computations to a handful of steps. Each Egyptian problem is a puzzle and its solution is an art.