008 = Height Matters and Dish Splatters

**Height Matters and Dish Splatters** is the eighth episode of A Problem Squared.

### Show Notes

Problems featured in this episode:

* Why are kitchen counters one-size-fits-all?
* Are the recorded surface areas of countries 3D?
* Why don't plastic things dry in the dishwasher?

Special thanks to:

Gareth and Kiruna (@garethandkiruna on TikTok and Pirate & Parrot TV on YouTube: Link)

Ed Warner from Motionspot (Link, Link and @themotionspot on social media)

Check out Podcasts in Color (Link) for an exhaustive and excellent list of podcast recommendations.

And for Bec's 5KTS t-shirt, head here: (Link)

### Summary

The first problem came from Manik (spelling unknown) whose brother and his wife both struggled to use their kitchen counters, one of them finding the counters too low and the other finding them too high. Bec mentioned that people often perceive her to be shorter than she actually is. She had heard about rise-and-fall counters from Gareth and Kiruna (links in the show notes), and Gareth mentioned rise-and-fall counters. Ed Warner, the founder of Motionspot, explained some solutions they have created for people of different heights who use the same kitchen. Matt gave Bec's solution a ding.

Phil Chapman (spelling unknown) asked whether the areas of countries take into account their topography, or whether they are calculated as if the country was a section of a perfect sphere. Matt tackled this problem. He took the UK as an example, and found that there were two different commonly given areas for the UK. An academic Matt spoke to wondered if this discrepency could be caused by the use of two different map resolutions. Matt explained the related coastline paradox (in which the length of a coastline depends on the length of the ruler used to measure it), but said this could not cause the discrepancy, because although would cause the perimeter of the country to be poorly defined, the same would not be true of the country's area. Matt was unable to find out who actually performed the two different measurements of the UK's area. However, Matt was able to find an area for Australia calculated by Geoscience Australia. They told him that their calculations did not take Australia's topography into account.

Matt then wanted to find out how large of a difference topography would make if it was included. He found that Alastair Ray (spelling unknown) had previously attempted to calculate this for a few different areas in Scotland, Switzerland, and Liechtenstein, but it seemed that the coastline paradox was occurring here, causing the area to differ depending on the resolution of the data used to calculate it. Due to how long the problem was taking and its visual nature, Matt decided to turn this into a video for his Stand-up Maths YouTube channel, and requested a half ding for his progress. Bec gave him a "di".

Laura (spelling unknown) asked why dishwashers do not dry plastic things. Matt conducted an experiment with his dishwasher to see what things would dry and which would not. His guess was that plastic's lower heat capacity (distinct from temperature) caused it to fail to dry. His wife Lucie Green thought it was something about the plastic's surface that caused it. Bec agreed with her but thought it might also be also be caused by the fact that plastic things more often have a concave shape. Because of the difficulty in solving the problem they asked for help from the listeners and did not yet offer a solution.

### AOB & Updates

As a follow-up to the previous episode a listener named Colin (spelling unknown) had sent in photos of themselves with several of Australia's big things from a previous trip.

Bec mentioned she had filled in the front of her £5,000 t-shirt (and had started on the back), and there were still squares available.

Bec pointed out that she and Matt had failed to mention James Bond in episode 007 of the podcast, and someone on Twitter had informed her that the first two characters in James Bond's code number are in fact letter O's, not zeros, though they are in reference to zeros.

In light of the Black Lives Matter movement, Bec recommended a podcast called Into America, an episode of This American Life (which may have been either We Are in the Future or Here, Again), an episode of Science Vs, an episode of Reply All, and the website Podcasts In Color.