The “Square” shape is a favored member of a special group of professionals and gentlemen in this two-dimensional world. The books narrator’s name is A-Square’s and he comes from this group.
Men are polygons with various numbers of sides, but women are simple line-segments. Women are required to make a noise if they move so they will not bump into the shapes. Classes are distinguished by the "Art of Hearing", the "Art of Feeling", and the "Art of Sight Recognition" or even just the sound of one’s voice.
The first seven chapters of the book considers existing in a two-dimensional universe, but then A- Square dreams about a visit to a one-dimensional world called “Lineland”. The inhabitants of this world can’t see A-Square as anything but a group of points on a line and they themselves exist only as just points.
After this dream A-Square is visited by a three-dimensional sphere named “A-Sphere” who has come from a 3-dimensional world. A-Sphere appears to A-Square but he still only looks like a circle to him. A- Sphere levitates both of them, up and down, and shows him what 3 dimensions look like. The two of them discuss the possible existence of a fourth, fifth and sixth dimension.
A-Square returns to his dimension, anxious to tell other about the other dimensions, but makes no progress in convincing the others of what might be possible, and he winds up in prison for what he is saying. Seven years after being imprisoned, A-Square writes out the book Flatland for a future generation so that they can see beyond their two-dimensional existence.
“Attend to your Configuration.”
― Edwin A. Abbott
