I give you two problems to soften your head.
Please click → topology(Question)
p.1: This problem is to find companion. First, I show you an example. If the earth was made of rubber clay, it would become a paper-like plane when extended with a stick. Things that can be deformed without cutting are referred to as "the same companion" . So the earth and the paper are the same companion.
p.2: This is 1st Question. There are 11 items. Please classify them into 4 types of groups. Human is one of the items, so please classify it. If you are not sure, see the hint on the next page.
p.3: Look at the illustration where the laundry is hanging. Sunlight enters through a hole on one side and the light-spots appear on the ground. Classify according to the number of holes through which light passes.
p.4: The second question. Do not cut the circle, but transform the left object into the right object. It seems impossible when you think about it, but it is possible. It may be faster to actually try and use clay than you solve the problem.
Please click → topology(Answer)
p.1: This is the answer. You can almost understand by looking at the hint. Do you know which group humans classify into? First, consider how many holes there are in humans. On the face, two eyes, two nostrils, one mouth, and two ear holes, a total of seven? Strictly speaking, the eyes, nose, ears, and mouth are connected somewhere, but dead ends are not counted. As with wine glasses, dents can be flatten, even if they look like holes. So, there are a total of three on the face(two nostrils and one mouth). How many are in your body? Yes, there is only one anus. Then, look at the picture of the clothesline. Same as a T-shirt. The hole in the neck' part corresponds to the mouth, the two holes through the arms correspond to the nostrils, and the hole of the torso's part corresponds to the anus. So a T-shirt and humans are same companion as the three green objects.
It is said that " humans is a thinking tube". Actually humans has one tube from the mouth to the anus. This tube is inside the body, but inside the tube is actually the outside world. In other words, the inside of stomach and intestines are inside the human body, but outside the body. It sounds logically inconsistent, but it's true.
p.2: This is the answer to 2nd Question. Looking at this, you may wonder what it is. You might say that twisting is unfair.