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first I have to say how surprised I am that I actually had fun reading this story, I even laughed with it. It's incredebly smart and full of irony. There is a connection to Galileo, we see someone who for the first time sees that the known world is kind of inacurate, and we have the contrast of what would have happened if Galileo would have gone against the Church's claims, his knowledge lost to us and his later proposals would have never taken place. At least Galileo had the help and complicity of his daughter, but the Square didn't have that luxury, even his brother could not believe his story. The Square is left alone and discouraged to prove his experience. 

I also noted a relation with a Brave New World in terms of the society in Flatland, even a bit of Gattaca, although deliciously misogynist. And the humbleness of the Square and how he addressed the reader reminded me a little to Alexander DeLarge, with the difference that the Square is not trying to manipulate but to ilustrate. Another thing that catched my attention was that just like in the fairytales, we see that physical imperfection is a synonym of evil.