## Tuesday, July 3, 2018

### A Favorite Space?

Barnes & Noble always has a number of quirky (relatively-inexpensive) 'popular’-style math books scattered around the store giving introductory samplings of a variety of math topics — usually the books are from Britain, often from publishers I’m not familiar with, and I often don’t find them very appealing, but occasionally do.

One I picked up recently is called “Math Hacks” by Rich Cochrane, which, once you get past the first couple dozen topics (out of 100 total), touches on some slightly more advanced topics than is often the case.  I’m enjoying the range/variety of topics mentioned. On the downside, only 1-2 very pithy pages is devoted to each subject, so if you already know the topic, you won’t gain much (if anything at all), and if you don’t already know the topic, you’re not really given enough to grasp it well, despite the over-hyped pitches made for the volume. So I don’t really recommend it other than as a source to dabble with, that might prick one's further interest in some given area.

At any rate, today I ran across “the illumination problem” in it (#73 of the 100), something I’ve mentioned here in the distant past and had forgotten about as an interesting and non-abstract geometric conundrum — it deals with configuring a room of mirrored (light-reflecting) walls in such a manner that a point light source within the room does NOT fill the entire room with light, but leaves some area(s) in the dark.

When I previously posted about it, it was to mention George Tokarsky’s 26-sided polygonal room solution to the problem in 1995, which led in turn to D. Castro's similar 24-sided solution below... a  space that I could imagine Evelyn Lamb enjoying ;)
 via HERE (If light source is at point "A" then point "B," amazingly, is in the dark.) There are other solutions (not all polygonal) to the problem, and the Wikipedia take on it is here:
https://en.wikipedia.org/wiki/Illumination_problem

…meanwhile the Numberphile treatment here: