Flatland is a satirical novel, written by Edwin Abbott Abbott, that depicts a nightmarish dystopia in a two dimensional setting, populated by living geometrical figures. A mathematician, called A. Square, describes his world, Flatland, a society that is strictly divided in social classes, resembling Victorian England.

The government of Flatland is administered by a cabal of many-sided polygons who promote a social hierarchy that ascends gradually from straight lines (women) to circles (priests). In between are irregular or isosceles triangles, the soldier and the working class; equilateral triangles, the tradesmen; squares and pentagons, who represents the professional classes, such as lawyers and mathematicians; and polygons of more sides, who enjoys the status of nobility.

In Flatland, evolution is not only a biological fact, but also a state policy. “It is a Law of Nature with us” writes A. Square, “that a male child shall have one more side than his father, so that each generation shall rise one step in the scale of development and nobility.” To assist nature, the ruling circles engage in selective breeding and extermination. Irregular figures are imprisoned, enslaved or destroyed, and surgery is performed to correct genetic deformities. Due to the prejudices and policies of the government, the political climate is ripe for revolution, so that Flatland suffers from many rebellions and outbreaks.

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.

In this context, A. Square recounts his adventures as he discovers an extra dimension. Guided by a three-dimensional cube, Square and his society cannot comprehend the idea that an extra dimension can even exist. However, an algorithm of sorts provides the proof necessary that any dimension has an extra one. The comparisons among one-, two- and three-dimensional worlds bring to light our attempts to understand four, five or even six dimensions in our universe. Square will try to enlighten his society, even in a disguised and apparently safe form in the beginning, but he is destined to fail against the short-sighted world of Flatland: the court system and social hierarchy firmly reject Square’s accounts of a universe that appears differently from their perception.