Discover Euler's number hole.

 Discover Euler's number hole.


A sharp vertex means, mathematically, that the exterior angle is large.


The exterior angle of a triangle is 120°, and the exterior angle of two vertices formed after one vertex is cut off is 60°...


Even if you continuously cut out one vertex and change the shape of the polygon, the sum of its exterior angles does not change. This invariant value is called Euler's number (Eulerian who showed that there is a close mathematical relationship between the value of v-e+f, the number of vertices, the number of edges, and the number of faces).



A rock falling from a mountain maintains the Euler's number, which is the relationship between the number of vertices, the number of edges, and the number of faces, as long as there is no hole, thereby maintaining the sum of the sharpness. However, if a hole is made while the stone is rolling down, the relationship between the Euler numbers changes, and the sum of the sharpness changes accordingly. For example, if there is one hole, the Euler number is zero. This is called mathematically 'the topological property has changed'.



So is life. The angles and sharpness that exist within us not only pierce me but also hurt those around me. So, the sharpness has to be cut by oneself and made into a round shape.


Just as a sharp stone rolls to and fro and becomes a round stone while it is terrified and cut, so is the character of a person.


As you endure the storms and hardships of time by bumping and breaking between people, at some point, you become round and soft like a stone. That is the time when the character matures.


Nevertheless, when I see the square shape of the past sometimes popping out, I feel the inevitable human imperfection. Even if a person matures, the sharp part does not disappear at all, but the sharpness is divided into several sides and the sharpness is dulled, and I think that it still exists somewhere deep down there. At that time, most people feel frustrated that their maturity has stagnated.


​


As the stone rolls and breaks, and a hole is made, the relationship of the Euler numbers changes, and the sum of the sharpness changes accordingly. It means that the nature of the stone changes by leaving a hole in the stone.


No matter how much a person rolls and breaks, its essence is difficult to change, but like a hole in a stone, when a person encounters a change, it becomes an opportunity to mature oneself one step further. It can be said that it is a change of topological nature in human life.


When we are weary of life, we also need something to change our topological nature. Like a hole for a stone, I wonder if we can truly change when we realize what that hole is that can transcend our own reality.


​

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