![]() My favourite solution was this one from Mike Lawler’s son, just because (unusual for social media) we get to see the entire thought process, including the bits where he gets stuck.” ![]() The design reminds me a lot of a stained-glass window in a chapel. “ This one,” Catriona says, “is actually featured in Alex Bellos’s latest book, which I think is very cool. What fraction of the rectangle do they cover? The Trinity Quartet All four triangles are equilateral. We spent some of the quieter moments of the day trying to figure out all the patterns, and I made this puzzle on the train home.”įunny coincidence! When I taught in Birmingham, one of our spectacular students taught this fact to me and other faculty. “I sat down next to somebody at a training event in Birmingham,” says Catriona, “who recognised my name from twitter and proceeded to tell me his favourite geometry fact: the inscribed circle in a right-angled triangle with integer sides has an integer radius. “My favourite thing about twitter,” Catriona agreed, “is being able to do maths with people all over the world.”įour, Three, Two What’s the area of this triangle? “See the word replies not in English, but the mathematical solutions are totally understandable.” “ Maths is a unique(?) international language,” commented one fan on this one. “ This one is a bit of a hangover from all those semicircles-within-rectangles puzzles I made back in December!” says Catriona. Setting Sun, Rising Moon What fraction of the rectangle is shaded? The ones on Twitter are always glorious, Olympic-gymnastic-level feats of symmetry. ”Īlso, please note: my solutions to Catriona’s puzzles are uniformly plodding, and usually devolve into calculation at the end. “One of my favorites – which I would never have come up with myself – is this one, where the top part of puzzle is tessellated to create a. “ There are lots of ways to approach this,” says Catriona. The Pyramid with Two Tombs Two squares inside an equilateral triangle. It was actually based on an earlier puzzle that you featured in your first collection.” Spoiler alert: “One of the lengths is a red herring – you only need to be able to answer. “This is a bit of a trick question,” says Catriona. “There are lots of very nice replies, but I particularly like this animation where the various possibilities seem to flow around the one fixed value.” “Easily my most popular tweet ever, this one,” says Catriona. Transit Across a Purple Sun What’s the total shaded area? So, for your pleasure: eleven delightful excursions into geometry. ![]() Y5fbjqFzOOĪnyway, Catriona continues to decline my offers to put her in touch with publishers, but kindly picks out favorite puzzles to share here. Here’s a flick through my notebook to give a sense of my scribbles-to-puzzles ratio. It was another tantalizing glimpse of her fertile thought processes: In reply, Catriona shared a video snippet of her notebook. ![]() “This,” Baez noted, “is also what Feynman said.” “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. “Does she have a general theory? Or a nice bag of tricks? Or what?” “These problems can’t just pop into her head,” insists Gowers. “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.” Puzzles that elicit caps-lock, triple-punctuated expressions of wonder. These are puzzles that entice and entrance mathematicians of every stripe. So what is this meta-problem nagging at him?Ĭatriona Shearer is a math teacher whose Twitter account features homemade geometry puzzles. His to-do list is no doubt a catalog of deep and important mathematical questions. Dude’s a Royal Society Research Professor at University of Cambridge. Gowers, a 1998 Fields medalist, has done breakthrough work in combinatorics. “There’s a meta-problem,” mathematician Timothy Gowers recently mused, “that it’s vaguely on my to-do list to think about.”
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