• You can get a really good approximation of a sinusoidal curve from twelve equally-spaced line segments of slope 1/12, 2/12, 3/12, 3/12, 2/12, 1/12, -1/12, -2/12, -3/12, -3/12, -2/12, and -1/12, respectively.

This approximation, known as the rule of twelfths, rounds √3≈5/3​ but otherwise uses exact values along the curve.

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• Recently I’ve been spending my spare time doing two things: solving cryptic crosswords and playing Pokémon Legends: Arceus. The next logical step, then, is to try my hand at compiling my own cryptic crossword themed after the game!

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• Shawn Mendes’ song “Lost in Japan” has had me geographically confused since I first heard it covered by Scary Pockets. If you haven’t listened to the lyrics, the song is about a person who is thinking about their crush and the possibility of taking a last-minute flight to Japan to see them.

The question I can’t get off my mind is: where is the song supposed to be taking place?

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• The time it takes to properly roast a whole turkey is proportional to its weight to the ⅔ power. My old mathematical modelling textbook specifically recommends 45 minutes per lb2/3 when cooked at 350℉.

For a spherical turkey of uniform thermal conductivity α and density ρ, a precise formula has been derived:

t = \ln\left(\frac{2(T_h - T_0)}{T_h - T_f}\right) \frac{1}{\pi^2\alpha} \left(\frac{3}{4\pi\rho}\right)^{2/3} m^{2/3}

where the oven is set at Th and the center of the turkey needs to reach a temperature of Tf from T0.

The more general ⅔ power law does not depend on unrealistic assumptions about the turkey’s shape or thermodynamic properties; it can be derived from pure dimensional analysis and applied to turkey-shaped meat-based objects by fitting a curve to specific cook times used by chefs.

• The official title of Chief Mouser to the Cabinet Office is held by a cat in charge of keeping mice under control at the UK Prime Minister’s office at 10 Downing Street. The current incumbent is Larry.

It was once commonplace to employ cats as mousers, so Larry is not unique; the UK Post Office employed a cat named Tibs the Great for many years and Canada’s Parliament had its own cat colony.

• Since the ’50s, Alberta has engaged in a deliberate effort to prevent rats from entering the province. Fortunately, rats can’t survive in the wild in Alberta, so they have pest inspectors regularly check every premise within a 29 x 600 km control zone from Montana to Cold Lake. Pet rats are illegal.

The rat-free status of Alberta led to a Wikipedia edit war over whether the province should appear on a map of the brown rat’s habitat. At some point it was decided to remove the map entirely from the English-language entry for Rattus norvegicus, but its presence on other Wikimedia projects means the edit war still rages on to this day.

• Vessel Finder is a map showing the current location of container ships, cruise ships, fishing boats, and other nautical vessels. It aggregates data from automatic identification systems which all sufficiently large boats are required to be fitted with.

This website was all over the news this week because of the ship stuck in the Suez Canal.

• The length distribution of tweets has shifted in response to raised character limits, but it’s still the case that a disproportionate number of tweets use all the characters they’re given.

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• This construction is made out of five copies of That Simple Unit (TSU), an origami module attributed to Charles Esseltine. I found this a little tricky to fold and put together, but the end result was very structurally sound.

• “General particulars” is an excellent phrase that deserves to catch on more widely than its current context of legally-mandated notices on boats.

(Boats are required by international law to have a wheelhouse poster listing their “general particulars”, i.e., a list of statistics, properties, and other bits of information necessary to get a basic view of the vessel.)

• The head of a sunflower is actually hundreds of smaller flowers working together to attract pollinators. Each large yellow petal is its own individual flower, and the bits in the middle are tiny five-pointed flowers if you look closely.

Sunflowers share this property with the rest of the family Asteraceae, including daisies, dahlias, dandilions, and dozens of “damned yellow composites“. The heads of these plants can be called inflorescences, or flower clusters.

• Pokémon Gold and Silver‘s roaming legendary beasts move randomly from route to route instead of sticking to a fixed habitat. By analyzing their behaviour using the math of random walks on graphs, I can finally answer a question that’s bugged me since childhood: what’s the best strategy to find a roaming Pokémon as quickly as possible?

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• Not all 26 letters of the alphabet appear on BC license plates. Six are missing — and the reason goes all the way back to 1970, when BC switched from issuing sequential plate numbers to an alphanumeric system.

One [story] is that the stamps used by employees of the MVB for compiling licensing documents in 1960s only had enough space for ten (10) characters.

The other is that when the province upgraded the machinery at the Oakalla Plate Shop in the mid-1950s, it was designed to accommodate a maximum row of ten (10) different dies for each of the six columns that might be used in the license plate’s serial.

Regardless of which, if any of these stories is the correct one, the alphabet was broken into two blocks of ten letters with the first block comprising A, B, C, D, E, F, G, H, J, and K with “I” excluded as it too closely resembled the number one.

Christopher Garrish
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• This polyhedron is made from eight triangles and six squares made according to patterns by Fuse Tomoko. The construction relies on inserts to connect the faces and did not last long in Diggy’s paws!

• This polyhedron is based on a pattern in the book Kusudama Origami by Ekaterina Lukasheva.

• This polyhedron was made from thirty copies of the Penultimate Module with 108˚ angles. I used rather heavy square paper rather than the recommended 4:3 paper; as a result, the creases are thicker and the edges show some separation between the folded layers.

• This polyhedron is based on the “Vortex Dodecahedron” pattern in the book Exquisite Modular Origami. It is built from thirty identical modules, which I made from basic one-sided red origami paper.

• Brick pavements and tatami mats are traditionally laid out so that no four meet at a single point to form a ┼ shape. Only a few ┼-free patterns can be made using 1×1 and 1×2 tiles, but the addition of 2×2 tiles provides a lot more creative flexibility.

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• This polyhedron was one of my first modular origami creations, and the pattern is my go-to option to share with others. It is made from thirty Sonobe modules, although if you get bored partway through you can make a triakis octahedron out of just twelve units.

• Although I’ve left academia, Bojan Mohar and I have published a new paper in the proceedings of SODA exploring the “perimeter” measure that plays a key role in my doctoral research. It is mostly based on Chapter 4 of my PhD thesis.