Courtesy of xkcd.com
It’s Mid-May, that means it time to put away your serious things and time to start thinking about (what else?) math puzzles!
Alexander Bogomolny, of CutTheKnotMath, has curated an amazing collection of math puzzles, problems, and interactive lessons. I always love to do geometry problems to get by brain working in the morning, and Bogomolny has plenty to spare. For example, this morning I picked up Two Equilateral Triangle on Sides of a Square. I solved it quickly, and then checked the (6 different!) solutions he gives on the page, all of which were different from my (sort of lame) approach.
Here I am in economy class, meanwhile he’s using quadrances and the triple spread formula. Bogomolny’s clear and varied solutions make me recall how much geometry has passed through my brain at one point or another, and also make the problems an interesting tool for exploring different math concepts in the classroom. He posts a lot of his problems to Twitter; you can follow him @CutTheKnotMath to get your daily dose of puzzles.
For the more tactile puzzlers among us, several people have sent me links to the infinity puzzle, which are “a new type of puzzle inspired by topological spaces that continuously tile.” There is a nice write up from some of the the makers at The Nervous System Blog, a blog about generative design. The puzzles are designed that they can be done right-side-up and upside-down and have no edges, but rather edge identifications.
Recently our friend of the blog, Mike Lawler from MikesMathPage, did a lesson in topology with his kids with the infinity puzzle as a jumping off point. Lawler and his crew determine the actual edge identification for their puzzle. Is it a Möbius strip? Is it a Klein bottle? Find out.
At the blog fivethirtyeight.com, Oliver Roeder curates a column called The Riddler, where really tricky but fun math problems are waiting to nerd snipe you. I particularly enjoyed the minimal urinal problem: what’s the minimum number urinals so that N people can optimally urinate? It’s much harder than it looked at first. This optimal urinal problem also showed up on the companion blag to xkcd a few years ago.
I appreciate that Roeder splits his riddles into Riddler Classic (to do while you’re on a long flight) and Riddler Express (to do while you eat breakfast). You might try the classic problem from a few weeks ago, which asked, how many decimal numbers are equal to the average of their digits?
Anyhow, if you’re headed to the beach, meeting friends for a beer, or just going for a walk in the woods, these puzzles are sure to delight everyone you meet, without exception. So definitely keep a few in your back pocket at all times, starting now. And please pass on worthy puzzles to me @extremefriday.