006 = Squaring Shirts and Testing Toasters

****Squaring Shirts and Testing Toasters**** is the sixth episode of A Problem Squared.

### Show Notes

Support us on Patreon! (Link)

Submit your data for our toaster investigation (Link)

Mike Hill wrote up his calculations as an official report. (Link)

Energy Scavengers: Static Electricity Could Power the World (Link)

International Electrotechnical Commission standards 60065 (Link)

Limmy's channel. (Link)

Limmys Show: Whats heavier a kilogram of steel or a kilogram of feathers (Link)

### Summary

#### Squaring shirts

Bec posed a question to Matt about fitting 500 regions onto a T-shirt, based on the million dollar homepage, where people could buy some pixels on a homepage to advertise themselves. Bec had an idea to do that with a plain white T-shirt, where she'd sell a region on the T-shirt for £10, where her followers could buy a space and she'd draw something in that space for them, which would result in a £5000 T-shirt.

Due to Matt taking a little while for it, Bec also asked her brother Mike, who is also a mathematician, to come up with 500 parts on a T-shirt to see if they would match. Mike calculated that the shirt would be around 8500cm² (front, back and sleeves). But he chose to only use 8500cm² which, dividing by 500 pieces, comes up to 16cm² per square, meaning each square would be 4cm on either side.

Matt did it a different way. Seeing that Mike had calculated the upper limit, he mentioned that he didn't tell Bec how to fit all the squares on the shirt. Starting by calculating the dimensions of the T-shirt, he then proceeded to fill in all the squares. However, he first started with just the front and the back in a rectangular grid, where the best solution is 6.29cm², where every region was 30cm wide and 2mm tall.

He then thought it was too difficult to draw on that, so he took into account the ratio of the width to height to be as long to 1:1. He came up with a 3cm by 2.1cm grid, 10x23 on the front, 10x27 on the back.

However, this was all based on different measurements from Bec's actual shirt. Matt inputted them into his program (width of 42cm, heights of 60 and 67cm, front and back).

Near the end of the episode Matt's code found that for a men's medium-sized shirt Bec could draw 3cm by 3cm squares on the front and back

#### Clothes dryers and static electricity

Matt sought to determine how much of the energy used by a clothes dryer ends up bound to the clothes it drys as static electricity. He found that a normal clothes dryer uses about 3 kilowatts of power while it operates. Assuming it takes an hour to dry a load of clothes, this means it uses about 10 megajoules of energy per load. International Electrotechnical Commission standard 60065 said the most static electricity an appliance was allowed to discharge into a person was 350 millijoules, so Matt used this as an upper bound on the amount of static electricity that could be in clothes after they had been dryed. This meant that at most 0.00000324% (less than one in ten million) of the total energy used by a dryer ends up in the clothes as static electricity.

#### Testing toasters

Bec sought to answer several toaster-related questions asked by Limmy on their show. Based on observations of her own toaster and the toasters of other people on Twitter, she determined:

* The numbers on the dial do not represent minutes, and do not even have a linear relationship to toasting times. (In other words, toasting bread on "3" does not toast it for 3 times as long as toasting it on "1".)
* Whether or not turning your toaster too high (specifically to "5") could be a fire risk may depend on your toaster. (Bec did not actually test this for fear of causing a fire.)
* If one sets their toaster to "1" and turns it on, but then immediately turns it up to "3" while it is toasting, the resulting toasting time varies depending on the toaster.
* If one sets their toaster to "5", turns it on, waits as long as the "3" setting takes, and then turns the dial all the way down to "1" while the toaster is still toasting, the toaster will turn off immediately.

Bec wanted to experiment with a toaster that had two levers and one dial. When she asked if someone on Twitter had such a toaster they could test, Limmy said they had one, but preferred the mystery of not knowing the answer.

Matt created a Google Form that listeners could use to submit their own toaster data.

### AOB & Updates

* 003: Someone on Twitter said they thought Matt was correct about episode 003's audio encoding issue. Also, Bec's friend Ron said he thought he could change the audio file to fix the issue.
* 005: The person who had asked the question of how to fit their backpack with them on the tube gave Bec's solution to said problem a "ding".