Who A Square is
A Square tells the story of Flatland, a world with length and width but no height. He belongs to its four sided class and describes its customs with calm confidence. His pride in being a respectable citizen shapes both what he notices and what he accepts.
He is kindly but vain, and his account reveals prejudices that seem reasonable to him. Through his voice, Abbott makes the unequal treatment of women and the strict ranking of shapes visible.
A Square and the others in the story
In a dream, A Square meets the King of Lineland and tries to explain a second direction. He grows angry when the king refuses to imagine anything beyond his single line. At home, he dismisses his grandson's suggestion that a number's third power might have a meaning in shape.
How A Square changes
The Stranger from Space unsettles A Square by entering a locked room and appearing to change size. The visitor describes three dimensions, placing A Square in a position like the king's. His certainty begins to give way as he hears about a reality he cannot picture.
Questions
Who is A Square in Flatland?
A Square is the book's narrator and a lawyer whose four sides give him a respectable social position.
Is A Square good or bad?
He is kindly but vain, and he accepts cruel customs as orderly and reasonable. His limitations make him part of Abbott's satire.
How does the Stranger from Space challenge A Square?
The visitor challenges his belief that only two dimensions exist. A Square must confront the possibility that his sight does not reveal everything.
