I am sorry to report that December has now fallen across the land.
It is December on the beaches. It is December in the streets. It is very specifically and intensely December outside my bedroom window, where 3-foot death icicles dangle, ready to fall and impale me as I step out into the frigid December of it all.
(Yes, we’re loving Minnesota, thanks for asking!)
Where can we find warmth in this frigid time? Yes, yes, the Southern hemisphere, but more usefully: in the life-giving geometry problems of Catriona Shearer, Puzzle Magician.
Here are three of her favorites from November. Come, friend; heat yourself by this fire.
Why do I dub this one “stained glass”? Because it has the delicate and symmetric beauty of a stained glass window, obviously.
But why “sci-fi”? That takes more explanation.
On Twitter, acclaimed sci-fi author Greg Egan chimed in with a crucial point: as stated, the problem is under-defined, allowing for an infinite family of solutions. Thus, Catriona added another condition: the whole diagram has bilateral symmetry.
To see why this is necessary, check out the nifty animation that Greg created. I, for one, am eager to watch the sci-fi film where all stained glass windows rotate like this.
(Note to my fellow U.S. readers: please forgive the Britishism “trapezium.” Actually, scratch that: don’t forgive it, embrace it! Trapezium is an adorable word.)
Catriona explained the genesis of this one:
Alison Kiddle, who coordinates my local MathsJam, asked me a question at last month’s meeting: could I draw a trapezium so that when I drew in the diagonals the four areas each had a different area? Could I draw one where 2 areas were equal, or 3, or all 4?
I was pretty confident that I could, but [spoiler] after a fair bit of scribbling and failing to convince Alison (who is very good at asking questions!) I realised I shouldn’t have been quite so hasty.
Naturally I’d brought my felt tips to the pub, so by the time I left I’d made this puzzle from my discoveries.
I found this one the trickiest of the three. Indeed, Catriona says that these three are “in ascending order of difficulty (in my mind, at least).” She also explains, tantalizingly:
Unless I missed it, I don’t think anyone posted the solution I originally came up with. It’s unusual for me to feel like my method is unique!
As always, feel free to post your solutions in the comments (which means you should watch out for spoilers if you don’t want them)!