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

There is an ancient fable called "waiting for a rabbit" to the effect that there was a farmer in the State of Song during the warring States period. One day, when he was working in the field, he saw a rabbit running past him. He crashed into a big tree on the edge of the field, broke his neck and died under the tree. The farmer picked up a ready-made rabbit effortlessly.

Since the farmer picked up the rabbit, he has abandoned his ploughing and sat under the big tree every day, waiting for the next rabbit to hit the tree. As a result, instead of picking up rabbits, the fields were deserted! This fable comes from the pre-Qin work "Han Feizi". It is very popular and has been spread for more than 2000 years.

Photo Source: pexels2000 for many years, people always think that "waiting for the rabbit" can not be done, and the crime lies in the "guarding the plant"! In fact, the crux of the problem lies in the movement law of the rabbit.

If the road to the tree is what rabbits must go through, then what's wrong with "guarding the tree"? The rabbit's activities, in the long river of time and space, draw a strange track. There is no doubt that it is extremely slim to hope that this track can intersect again with the tracks of trees in time and space, which is precisely the tragedy of this farmer!

The following is a more subtle example that enables people to see the crux of the problem vividly. The example shows that if you can find out the law of rabbit movement, sometimes it is even wise to "keep"!

Leonardo da Vinci (Leonardoda Vinci,1452-1519) was a master of Italian Renaissance art. Leonardo da Vinci not only had deep attainments in painting, but also studied mathematics.

He once asked an interesting question of "hungry wolves beat rabbits": as shown in the picture, a rabbit is foraging at O, 60 yards (1 yard = 0.9144 meters) south of cave C, and a hungry wolf is now wandering A just east of the rabbit. Looking back, the rabbit suddenly met the hungry wolf's greedy eyes and had a premonition of disaster, so he hurried to his cave. Seeing that the delicious food was about to fail, the hungry wolf immediately stared at the rabbit and chased it at twice the speed of the rabbit. As a result, the wolf and the rabbit launched a life and death, soul-stirring chase.

Q: can rabbits escape their doom? Someone has done the following calculation.

With O as the origin, OA,OC is the x-ray axis and the length is 1 yard. Then OA=100,OC=60.

According to Pythagorean theorem, in Rt △ AOC:

This means that if the hungry wolf goes straight to the rabbit cave in the direction of AC, then because the speed of the rabbit is only half the speed of the wolf, when the hungry wolf reaches the entrance of the rabbit cave, it is only 116.6 yards away, that is, the rabbit is only 58.3 yards away from the hole. At this time, the hungry wolf who arrived at the mouth of the cave first could have stayed at the mouth of the cave and waited for the arrival of a good meal.

The above calculations seem flawless, and the conclusion is that the rabbit is doomed.

But in fact, this is wrong! It is impossible for a hungry wolf to go straight to the rabbit cave to "sit and wait". Its strategy can only be to keep an eye on the rabbit in motion, so that its own pursuit route becomes a curve, which can be deduced analytically:

This means that if there is no rabbit hole in the north, the rabbit will be caught by the hungry wolf when it runs to point B, 66 and 2 yards from the origin.

Fortunately, however, the rabbit hole is only 60 yards from the origin, and the rabbit has already entered the hole safely.

With the answer to the riddle of "the hungry wolf attacking the rabbit", the discrimination of "waiting for the rabbit" seems to be coming to an end.

Unexpectedly, some people later raised objections and doubted the authenticity of the story of "waiting for a rabbit".

The reason is: how could a clever rabbit bump into such a big tree stump? What happened to his big shrewd eyes?! You have a point! But the answer is yes.

To make this clear, we have to start with the function of the eyes. The visual function of the eye is interesting. One eye can see clearly the objects around it, but it cannot accurately judge the distance between the eyes and the objects. The following experiments can prove this very vividly.

Find two sharpened pencils and pick up one in each hand. Then close one eye and keep the tips of the two pens close together from far to near.

At this time, you will find a strange phenomenon: no matter how you concentrate, the tips of the two pens always crisscross! However, if you keep your eyes open, it is easy to aim at the tip of your pen.

The above experiments show that the position of an object can be accurately judged with two eyes, but not with one eye. So why can you determine the exact position of an object with two eyes? It turns out that the image of the same object in people's eyes is different! The following picture shows an image of a tunnel in both eyes, and the difference between them is obvious.

Now let's go back to the discussion of the rabbit hitting the tree.

The position of the human eye is different from that of the rabbit eye: human eyes are in front of each other and are very close to each other. On the other hand, the rabbit's eyes are on both sides of the head.

According to the measurement, the visual field per eye of rabbits is 189 °30 °, while that of human eyes is about 166 °.

However, because people's eyes are in front, the field of vision that can be seen by both eyes at the same time is about 124 °. The human eye can accurately determine the position of an object in this area. Although the rabbit eye can see anything around it, the coincident visual field of the two eyes is only 19 °, including 10 °in front and 9 °in the rear. Therefore, the rabbit can accurately judge the distance of the object only in a very small visual area!

It can also be seen from the picture above that even though the rabbit is acutely aware of the threat from all directions, it is sensitive to what is under its nose. Area), but can't see it at all!

Moreover, in the panic-stricken rush for life, it is impossible to say that he has already lost his head, and it is impossible to guarantee that the incident of hitting a tree will not happen.

Wen Yuan: a Mathematical Story Book for Children

Author: Zhang Yuannan Zhang Chang

Editor: Zhang Runxin

This article comes from the official account of Wechat: Origin Reading (ID:tupydread), author: Zhang Yuannan Zhang Chang

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.