Proof that there is no point n edge (n! = 4)

This is an answer to zhihu. I personally like this proof.

 

How can we prove that any six points in a plane cannot form a hexagonal structure?

If the entire hexagonal point exists, there must be one with the smallest side length.
The center will rotate 90 degrees counter-clockwise. Obviously, it is also the whole point. Similar definition ~, They are also the entire point.
As you can see, it is a smaller integral hexagonal, with contradictions.

 

This also indicates that the entire triangle does not exist. Because as long as there is a triangle, there must be a whole-point hexagonal.
It is worth noting that such proof can be promoted (n> 4 hours ). The following figure shows the Pentagon.

 

Proof that there is no point n edge (n! = 4)