Recreational Math

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Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
—David Hilbert

I was doing mathematics—arithmetic, at any rate—for recreation as early as age 6, although it was not until I got to junior high school that I encountered what is generally known as recreational mathematics. It was in junior high that I encountered a charismatic teacher, Mrs. Eunice Williams, who Equations and figuresgathered around her, Pythagoras-like, a group of talented math students and infected them with her excitement and love for mathematics. At least two students in my class eventually became professional mathematicians, and I studied computer science in graduate school and minored in math. In fact, when I had a rare opportunity to take a free elective in college, I chose a linear algebra course. In graduate school, one of my favorite courses was modern algebra. My dissertation was in automata theory, which comes perilously close to being a topic of recreational mathematics, which is how I viewed it while I was still an undergraduate.

I enjoy mathematical puzzles and problems of all kinds, although I don’t spend a lot of time working on them. Every so often, however, a problem really engages me—particularly if it can be generalized—and the topic becomes consuming. Working  on such a project helps me keep my mathematical skills sharp and gives me an excuse to do things that I wouldn’t normally do in the course of more ordinary work. 

It’s hard to say just what recreational mathematics is, other than to say that it’s not professional mathematics. A professional mathematician can do recreational mathematics, and an amateur mathematician can do professional mathematics, and it’s sometimes hard to determine who is doing what when. Mathematics with no obvious “use,” particularly if it has a strong aesthetic or brain-teaser component, is likely to be consigned to recreational mathematics. In fact, though, even seemingly “useless” mathematics tends to find utility eventually.

In this section of Lionel Deimel’s Farrago, you will find discussion of topics in recreational math where I have made some small contributions. I hope you enjoy reading these pages, and I encourage correspondence about these and related topics.

— LED, 11/6/2017

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Digital Invariants—definitions, observations and theorems about numbers whose digits, in some representation, have special properties (e.g., 153 = 13 + 53 + 33)

Curve-stitch Designs—arresting designs made from straight lines, whether generated by computer or (as was originally done) executed with colored thread and cardstock

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