Shulou(Shulou.com)11/24 Report--

If someone tells you that a point can always be found on the earth at any time, there is no wind at this point! You may be surprised by this, but it is true. Shrinking to a small scale may make you believe this even more.

As we all know, a typhoon is a big storm in the tropical ocean. it is actually a mass of rotating air over a wide range.

We often hear about typhoons in the news, saying that the wind near the center of the typhoon has reached force 12. This means that the wind speed near the center of the typhoon is 33 meters per second, which is equivalent to the speed of a high-speed train.

Photo Source: pexels what is more, for example, the 9th Typhoon Lekima (Super Typhoon) in 2019, the maximum wind speed near its center reached 52 meters per second.

However, in the center of such a violent typhoon, in the range of about 10 kilometers in diameter, because the outer air rotates so much that it is not easy to get into it, the air there is almost non-rotating, so there is no wind.

The following is a true report, this is an American meteorologist's vivid description of what he witnessed when he rode a typhoon reconnaissance plane into the eye of a typhoon in the Pacific Ocean. It will undoubtedly deepen your understanding of the strange landscape of Typhoon Eye.

". Soon, the edge of the rainless typhoon eye began to be seen on the plane's radar screen. After the plane bumped through the torrential rain, suddenly we came to the dazzling sun and clear blue sky. There is a magnificent picture around us: in the eye of the typhoon is a clear sky, 60 kilometers in diameter, surrounded by a cloud wall. In some places, the tall cloud wall stands straight up, while in others, the cloud wall tilts up like the grandstand of the stadium. The circle above the eye of the typhoon is 10 to 12 kilometers, which seems to be on the background of the blue sky. "

Look! In the roaring wind like the galloping of thousands of horses, there is indeed a fixed point of the wind.

The phenomenon of fixed point can be seen everywhere in nature and life.

In his book the Mystery of Science, Professor Tanaka of Tokyo University of Technology, Japan, mentioned an interesting thing: the teacher took a group of students to a temple to visit. The teacher put his head into the big hanging bell to observe the structure of the bell. A student was very naughty. In order to frighten the teacher, he tried to strike the big bell with the bell wood. As a result, instead of scaring the teacher and the female students next to him, he was startled by the loud sound of the bell.

Why did this happen?

Professor Tanaka drew a picture and explained that this is the same as filling a bowl with water and then tapping the edge of the bowl with chopsticks, we can see the ripples moving from around the bowl to the center of the bowl. At this time, some of the ripples in the center disappear because they cancel each other out.

A, B, C, D and E in the picture are actually the fixed points of sound waves. On the contrary, F, where the students stand, is the place where the bell vibrates the loudest, so the sound is naturally particularly loud.

Next you can play an interesting game.

Take two photos of the same person, stack the small photos on top of the big photos, and then you announce to the audience: there must be a bit of O in the small photo, which actually represents the same point as the point opposite to the big picture below.

Your audience will be skeptical about this. However, when you tell him how to find this fixed point, all their doubts will go away.

Let the big photo be the ABCD, and the small photo be ABCD. Extend the AB to point P, and circle through A, P, A, and B, P, B', respectively. Then the intersection point O of the two circles is the fixed point.

In fact, as you can see from the picture above:

This shows that the position of the O point in the large and small photos does not change, that is, O is the fixed point of the photo position transformation.

Look at that! How magical and intriguing the phenomenon of immobility is!

Another example is the flat map that can be seen in places such as shopping malls, with a red dot marked "you are here". If the label is accurate enough, then this point is the fixed point of the continuous function that projects the actual terrain to the map.

The earth rotates on its axis of rotation. The rotation axis is constant in the rotation process, that is, the fixed point of the rotation motion.

The study of fixed point systems began at the beginning of the 20th century, in 1912, when the Dutch mathematician L.E.J. Browell (L.E.J. Brouwerj1881-1966) proved that any one who transforms an n-dimensional sphere into its own continuous transformation has at least one fixed point.

This is the famous fixed point theorem.

For most readers, some mathematical terms in Browell's theorem undoubtedly need to be explained.

For example, shallowly speaking, that is, the "continuous transformation" of the original distance is very small, the distance after transformation is still very small. As for "n-dimensional space", this is an abstract concept.

Specifically, a straight line is an one-dimensional space, a plane is a two-dimensional space, an ordinary space is a three-dimensional space, and so on. Therefore, the line segment is an one-dimensional sphere, the plane circle is a two-dimensional sphere, the ordinary sphere is a three-dimensional sphere, and so on.

Although the strict proof of Browell's theorem is esoteric, some examples of Browell's theorem are very interesting.

Take a flat chassis and a piece of paper that covers the bottom of the plate. Each point on the paper corresponds to a point on the disk directly below it. Now pick up the paper and knead it into a small ball of paper, and then throw it into the plate.

So, according to Browell's fixed point theorem, no matter how the paper ball is rubbed or where it falls at the bottom of the plate, we can be sure that there is at least one point on the paper ball, which is just above the point at which the plate used to correspond. Although we are not sure where such a point is.

The above facts can be explained as follows: suppose the orthographic projection of the small paper ball on the disk is the region Ω 1. Obviously, the point corresponding to Ω 1 on the original paper must be directly above Ω 1, assuming that the orthographic projection of this part of the paper ball at the bottom of the disk is the region Ω 2, obviously Ω 2.

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.