It’s very common to have ear holes. Both women and men want to have ear holes and wear earrings to make themselves beautiful and handsome. Who knows, when the ear hole, and do not play ear hole body structure has been completely different, there has been a difference. Then you will ask, why is it different? Isn’t it just one more ear hole? Only mathematicians know the answer to this question. They said that this is not a morphological difference, but a mathematical difference. This is a knowledge of topology, which involves “Genus” and “directionality”. The following editor will introduce this magical thing to you.
Let’s take a simple example. Suppose we have a stretchable rubber ring and a double hole ring with two rings combined to form a symbol like 8. When we twist half of the rubber ring 180 degrees to form a twisted ring like 8. At this time, we can be sure that the twisted ring can never be a double hole ring. Although they look very similar, we know that their holes are not the same. The twisted rubber ring is still a hole, and the double hole ring is two holes, and this hole is the “Genus” in topology. When you understand the brief introduction of “Kuge”, you will know why the two people’s body structure is different after the ear hole. As you can imagine, people who don’t have ear holes and elephants are the same kind. They don’t have the difference in “defect”. People who have ear holes add a “defect”, so their body structure is completely different.
“Genus” is a factor to judge whether the material structure is the same or not. Another factor is “directionality” in topology. Directionality can be divided into “directionality” and “non directionality”. Let’s still give an example. Suppose we have a piece of paper. We twist the end of the paper 180 degrees, and then glue it to the head of the paper. In this way, we get a very magical thing – “Mobius belt”.
Why is it amazing? We use a pen to draw a line from the head of the paper, and draw along the direction of the paper. You will be surprised to find that we draw both sides of the paper, and finally we will return to the beginning of the line, which is “non directionality”. We simply glue the head and tail of the paper to form a ring, and draw lines along the direction of the paper from the head. We can find that the other side of the paper can’t draw lines, so this is “directionality”. Here, the nonorientable Mobius belt is actually a two-dimensional surface, not a three-dimensional one.
For these two knowledge in topology, it is very interesting and worth studying. It also involves the knowledge of spatial dimension. More examples, such as Klein’s bottle, are also things with an undirected magical material structure with a genus. There are many strange things in the world. The application of mathematical knowledge can make us understand the essence of the world better.