Flatland follows the journeys of A. Square, a mathematician and resident of the two-dimensional Flatland, where women - thin, straight lines - are the lowliest of shapes, and where men may have any number of sides, depending on their social status.

Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions-a revolutionary idea for which he is returned to his two-dimensional world.