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If one day you forget to bring your cell phone when squatting, you might as well pick up toilet paper and study it when you are bored.

It would be nice if there was Sudoku on the roll.| Pixabay, don't underestimate the roll of paper in the bathroom. We may be able to learn math with toilet paper. What's even more outrageous is that people have been arguing for decades about how to place a roll of toilet paper.

How long is a roll of toilet paper? If you want to know how long a roll of toilet paper is, what's your solution? Except for unwrapping a roll of toilet paper the way mom would punch it, maybe next time you can try calculating it.

I want to know how long a roll of toilet paper is.| Giphy In the eyes of math teachers, this is just a simple calculus problem. Learn how to do this, and the next time you squat, you can easily figure out how much toilet paper you have left.

From the very beginning, we can think of toilet paper as a paper tube with radius R, which is wrapped with n layers of paper, which can be regarded as a set of n layers of rings. The total thickness of the paper is D. The thickness of a piece of paper is h.

Therefore, the radius of the first layer is R1=R, the second layer R2=R+h, the third layer R3=R+2h, and the ith layer becomes Ri=R+(i-1)h.

So, to calculate the total length of the paper, L1, we just need to calculate the circumference of each circle and add them up. It's very simple.

A simple summation problem (omitting the middle calculation), but the case of the paper roll is more complicated than this, because the radius of the ring increases as the paper winds. Instead of looking at it as a ring layer by layer, it is better to look at it directly as a spiral, and calculate the total length of the spiral by the angle of rotation. Then add up all the angles the paper towel has been rotated.

At this point, we have a formula for calculating the length of the paper, and we just need to insert all the values that are easy to measure.

It is worth noting that if you think it is difficult to calculate how thick a piece of paper is, you can stack 20 pieces of toilet paper together and divide it by 20!

There are more ways than difficulties!| Giphy A roll of standard toilet paper (paper tube radius 55mm, paper thickness 20mm, sheet thickness 0.36 mm), paper length is about 22907 mm. You can also take a ruler to the toilet and count the length of toilet paper in your home.

The answer to this estimate has also been verified. According to the manual count of the scientific editor next door, a roll of toilet paper has a total of 167 cells. If this is calculated, each cell separated by dashed lines is 13.7 cm.

After verification, the results were indeed accurate!| Bringing Science Home Is it useful to use toilet paper to learn simple modeling and calculus? Mom's gonna walk you to the bathroom all night.

How do you keep your toilet rolls? Do you put toilet rolls in or out? Why not?

In 1986, columnist Landers publicly stated in a magazine that toilet rolls should be placed inward. Her views were so controversial that Landers received 15000 letters discussing the issue that year.

For decades, people have been arguing about this issue, and everyone has their own opinions, from aesthetics to comfort and convenience.

Fight! Fight! Those who put it outward feel that it is more convenient to take out the number of squares they want. And if the paper roll is placed inward, it is easy to touch the wall when it is taken out, and it is stained with bacteria and dust.

Inward-facing people, on the other hand, believe that hiding the end of the toilet paper will keep it tidy and prevent children or pets from pulling the whole roll apart.

Perform a roll paper vanishing spell!| Giphy In various surveys, on average, about 30% of people choose to face inward, and about 70% choose to face outward.

If you happen to meet someone who agrees with you, you may be lucky because it will avoid some arguments. Studies have shown that arguments about which way toilet paper should be turned can occur in homes, businesses and public places, and can really affect mood.

The survey found that couples actually argue over this issue. At amundsen-scott station, where dozens of people live together, complaints have been filed about where toilet paper faces.

Toilet paper: ? It's none of my business. Don't cue.| Pixabay found that 24 percent of the 700-plus people who put toilet paper outward were annoyed because it was not oriented correctly, and 27 percent corrected the orientation of toilet paper in a friend's bathroom.

If you think this question makes no sense, then…what else? Toilet paper whether to put outward or inward, shower should wash hair first or shower first, socks should roll outward or inward, seems to be very suitable for the toilet when considering the problem.

And because of this, it has spawned some more thoughtful designs. For example, put two roll paper racks in the toilet, one facing inward and one facing outward, without affecting each other. Or can rotate toilet paper rack, automatic paper machine, etc.

For the sake of world peace, we'll have to put two toilet paper holders.| Wiki Everyone's way of picking up paper, is it unique? I have to admit that toilets are closely related to our health. From the toilet, we can see a person's eating habits, intestinal health and kidney diseases. So in the future, toilets may be important places to collect personal health data.

But there is a problem: because toilets are often shared by several people, user identification becomes an important issue if you want to collect information.

A lot of health indicators can be seen in the toilet.| Pixabay is definitely not going to work with cameras and microphones in toilets because of privacy. Manually entering personal information every time you go to the bathroom doesn't seem to make sense, and scientists have suggested that you can extract everyone's DNA from faeces, but that's time-consuming and expensive, and it's not easy to do.

Japanese scientists have suggested that we can identify people who go to the toilet by pulling toilet paper!

？They consider that in a private space like the bathroom, perhaps everyone has a unique way of getting paper. So they put wireless gyroscopes in toilet paper holders, measured the angular velocity of pulling toilet paper, and trained them with lots of data to identify who went to the toilet.

It turned out that the gyroscope sensor's recognition accuracy rate was 69.2% in the actual five-person home scene. However, this amount of data is still too small. If trained with more data, the device can recognize more accurately.

You can tell who you are by pulling the roll of paper.| Giphy doesn't look like much use, but going to the toilet is a serious matter, and roll paper can be regarded as a great invention. Ancient people used to clean themselves with leaves, grass, shells or moss after using the toilet. It was not until the 19th century that roll paper came into the assembly line. People are also embossing and improving materials to make toilet paper more comfortable, durable and environmentally friendly.

Even if you don't have a phone when you go to the bathroom, you can still look at the roll of paper more often and maybe you can play with it.

Really play with flowers. A cold knowledge: tissue paper (all kinds of tissue paper) and toilet paper (roll paper) are two kinds of paper. In addition to the difference between the volume and the volume, the hygiene standards of the two kinds of paper are different.

References:

https://docs.qq.com/ doc / DU1hZb2taT1h0Rkhy

This article comes from Weixin Official Accounts: Bringing Science Home (ID: steamforkids), by Skin

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