The Mathematics of Various Entertaining Subjects

The subtitle of the book, Research in Recreational Mathematics, is very appropriate, for most of the papers in this collection are indeed research rather than simple recreations. The concepts are based on topics generally considered recreational mathematics, yet the treatment is in the form of research papers.

For example, there is the paper “Tic-tac-toe on Affine Planes.” It begins with the simple game and then establishes a set of three axioms for an affine plane that is a set of points and a set of lines. Which, in the simplest form is what the basic game is. By expanding it out and allowing a line to be a curve that wraps around, the game becomes much more complex, both to play and to analyze. A game where all is known becomes complicated and challenging.

There is no puzzle more popular than crossword puzzles, which are a staple in the regular print media as well as a daily mental challenge in the lives of millions. In the paper “Analysis of Crossword Puzzle Difficulty Using a Random Graph Process,” a probability model is developed that can be used to analyze the inherent difficulty of specific puzzles in their raw form. Simulations are also used to create data supporting the value of the model.

There are 17 papers in this collection, covering many areas of recreational math and games. Applications sneak in as well, in the paper “Error Detection and Correction using SET©,” the card game is used to model error correcting codes, a necessary feature of ensuring error-free electronic transmission. In other words, keeping civilization as we know it functioning.

Even if you are someone that does not consider recreational mathematics to be real math, there is no denying the conclusion that this is real math. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.