Set in a world of only two dimensions inhabited by sentient geometric shapes, the story follows Arthur Square and his ever-curious granddaughter Hex. When a mysterious visitor arrives from Spaceland, Arthur and Hex must come to terms with the truth of the third dimension, risking dire consequences from the evil Circles that have ruled Flatland for a thousand years.

Set on the eve of Flatland's first mission into their 'outer-space,' the story presents the intriguing mysteries of triangles with angle sums greater than 180 degrees and flipping into dimensions that are literally out of this world.