Having fallen under the spell of Catriona Shearer’s geometric puzzles again, I thought I would present the latest group assembled by Ben Orlin, which he dubs “Felt Tip Geometry”, along with a bonus of two more recent ones that caught my fancy as being fine examples of Shearer’s laconic style. Orlin added his own names to the four he assembled and I added names to my two, again ordered from easier to harder.
(Update 4/16/2020) Ben Orlin has another set of Catriona Shearer puzzles 11 Geometry Puzzles That Drive Mathematicians to Madness which I will leave you to see and enjoy. But I wanted to emphasize some observations he included that I think are spot on.
“There’s a meta-problem,” mathematician Timothy Gowers recently mused, “that it’s vaguely on my to-do list to think about.”
Gowers, a 1998 Fields medalist, has done breakthrough work in combinatorics. Dude’s a Royal Society Research Professor at University of Cambridge. His to-do list is no doubt a catalog of deep and important mathematical questions. So what is this meta-problem nagging at him?
“HOW DOES CATRIONA SHEARER DO IT???”
Catriona Shearer is a math teacher whose Twitter account features homemade geometry puzzles. But “puzzles” perhaps undersells them. These are puzzles that entice and entrance mathematicians of every stripe.
Puzzles that elicit caps-lock, triple-punctuated expressions of wonder.
“I don’t think I’ve ever seen anyone in my entire life,” says the mathematician Mike Lawler, “who has an eye for neat geometry problems like Catriona Shearer does.”
“These problems can’t just pop into her head,” insists Gowers. “Does she have a general theory? Or a nice bag of tricks? Or what?”
“Yesterday I read a tweet of hers,” chimed in John Carlos Baez, a leading category theorist, “where she said she’s not as creative as some people seem to think: she keeps using the same tricks over and over again.
“This,” Baez noted, “is also what Feynman said.”