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this is not proof, though. can you prove it in general?
Welcome to the forum.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
You must be careful, but many proofs can be made by pictures alone. You must use caution because picture proofs can charm your intuition which can be easily fooled and furthermore, it is easy to ignore important conditions to your theorems!