Matt still frequents the Step And Conquer, though it has been converted into winter mode. He has also installed a fire pit (the barbecue with its legs taken off), which broke his fire pit cycle. Bec is invited to burn her evidence in Matt's fire pit.
Bec has a new pet: A really cute little hamster named Pudding. She has put a tiny easel with a tiny notepad in his enclosure so he looks like he's doing a tiny flipchart gig.
Bec proposes the format "A Pudding Squared" where simple hamster problems for children are posed. This episode: Hamsters in the wild can run up to 9 km. Pudding's little wheel is 14 cm in diameter. How many rotations does Pudding have to run to get the same exercise as he would get in the wild?
Sharks constantly grow new teeth. What is the fastest rate you can pull their teeth out so that they always have at least one tooth (assuming one tooth at a time)?
Bec likes this problem because of her obsession with teeth, described in problem 001-2. Shark have a conveyor belt of teeth in their mouth. Nobody really knows how many teeth shark have, or how fast they regrow. Bec's best guess is anywhere between a day and a few weeks. She that sharks have roughly 49 teeth in their outer layer, and that each tooth is replaced once a week, which makes a tooth every three or so hours, or every hour during working hours (including weekends), but you take lunch time off.
A "ding" by Bec
I have a question: A lot of people are infected with covid, but a virus is also very small. That made me wonder: How many litres of the virus are there? I guess it can't be that much.
A cell is about 10'000 times smaller than a human. Bacteria are about 1000 time smaller than our cells. A virus is around 1000 times smaller than bacteria. Matt estimates one virus to be 150 nm across. Scientists estimate 400'000 viruses per ml of fluid. Matt estimates 2 l of said fluid per infected person, 300'000 new cases per day, and an average infection length of 2 weeks, meaning there's just over 4'000'000 people currently infected.
Combining all that gives us roughly 3.3 quadrillion (3.3e15) virus cells. Stacking them like tiny Ferrero Rochers (see problem 011-2), this gives us roughly 8 ml of virus, about a teaspoon. No matter how you tweak the numbers, it'll fit into a shot glass.
Footnote: Even though virus particles are tiny, it's still worth wearing a mask. The viruses in the air are carried by substantially bigger droplets.
An "I'm happy with saying that's definitely a problem solved" from Bec
I used to think of big fluffy jackets as being inherently warm, but of course they're really just insulation against the cold. How hot does it have to be outside before wearing a jacket will help you stay cool? Does it depend on how long one spends in the heat?
Our core body temperature is around 37°C, Bec's slightly cooler 🕶️. Naïve answer: At any temperature above 37°C, the jacket insulates us against the outside heat. But biology is a lot more complicated. The body constantly generates heat, and the jacket will prevent sweating.
Bec was confused by firefighters and their calendars, so she asked Dr. Rohan Francis, who then asked a firefighter. The jackets allow the firefighters to walk through flames, but only for a certain amount of time.
Bec has access to both a fluffy jacket and an infrared sauna for experiments, but she is not sure how to experiment. She asks listeners to contact her with ideas.
I recently bought Cheese in Tesco's in a more unconventional shape. Tesco claims that this squarer packaging uses 40% less packaging than its previous rectangular block. [The author forgot to measure an old block of cheese for comparison, but includes measurements for the new block.] Firstly, is Tesco correct in saying there's a 40% reduction in plastic? What would be the most efficient packing solution that minimizes wasted space and cuts down on plastic? Which products would have the greatest improvement in reducing packaging by just changing its shape?
Matt does not think there is a sensible shape for the old packet that would lead to a 41% reduction in surface area. The only real option would be a large thin pancake of cheese, which seems unrealistic. There must be something else going on.
The best way to package would be a cheese ball 9 cm across. A sphere has the smallest surface area of all shapes. However, wrapping and stacking them becomes worse (as discussed in problem 011-2). So instead, Matt wants a shape that stacks well but minimizes surface area, which is known as the Kelvin problem. Lord Kelvin claimed in 1887 that a truncated octahedron was the optimal shape. In 1993, he was proved wrong with a weirder shape.
But for transport in a cuboid box, you want a cuboid shape, so Tesco's approach is actually the right one. Matt suspects that optimizing the shape for transport might be a bigger deal than the actual amount of plastic, but that's hard to describe on a block of cheese.
Matt Bec suggests contacting Tesco's. wants to measure some cheese. Listeners are encouraged to ask Tesco's as well. Bec suggests the hashtag #cheesecoverup.
Matt wants to send out christmas cards for patreon supporters of the podcast, but he doesn't know what to put on them.
Matt has sent math-pun-ish christmas cards to his patreon supporters for the past four years, which he shows Bec. Since the podcast patreon goal (from episode 003 (note)) was met, he also wants to start the same tradition for this podcast. He requests help from Bec for christmas card ideas. The new patreon goal for the next year of APS will be 314 patrons, or roughly pi hundred.
A lot of problems are maths based, which is great but Bec's specialty is more creativity-based. Bec wants more of those. Don't stop sending in the maths problems though!
Listeners are encouraged to fill in the survey linked in the episode description, so Matt and Bec get some good feedback for the show.