Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4571 + 2426 = 6997

## Harry Potter Book Sizes

Prof. Alan Kaminsky
Rochester Institute of Technology -- Department of Computer Science

After publishing the first four Harry Potter books, author J. K. Rowling was on a roll. The book sizes were growing exponentially, and the fifth book was projected to be over 1,800 pages long, as shown on the graph below.

However, when the fifth Harry Potter book was published, it was only 870 pages long. Clearly, Ms. Rowling had started to run out of steam. Indeed, the graph below shows that Ms. Rowling's output had peaked and would now diminish, with the sixth and seventh books being only 563 and 428 pages, respectively.

The sixth Harry Potter book turned out to be 652 pages long instead of the previously-predicted 563 pages -- an error of about 15%, which is pretty darn good for prognostications of this sort. Although Ms. Rowling apparently had a bit more steam left in her than expected, the graph below still shows that Ms. Rowling will continue to lose momentum, with the seventh book being only 545 pages.

Foiling the previous prediction, Ms. Rowling churned out 759 pages for the seventh and last Harry Potter book -- 39% more pages than she was supposed to. Her burst of energy on the sixth book apparently continued into the seventh, although she didn't quite re-attain the peak she reached on the fifth book. The graph below is the culmination of this years-long research project. All is well.

Technical Note: The first graph is a least squares fit of an exponential function to the four data points. The second graph is the exact rational function (ratio of two polynomials) that passes through the five data points. The third graph is the exact rational function that passes through the six data points. The fourth graph is the exact rational function that passes through the seven data points. The displayed coefficients have been rounded to three significant digits. Calculating the correct y values requires using the full-precision coefficients.

 Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4571 + 2426 = 6997