Flatland: A Romance of Many Dimensions (Illustrated)

(Illustrated) This book is hardly complete without the mathematical illustrations of its author Edwin Abbott Abbott (A Square).

Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as "a Square", Abbott used the fictional two-dimensional world of Flatland to offer pointed observations on the social hierarchy of Victorian culture. However, the novella's more enduring contribution is its examination of dimensions, for which the novella is still popular amongst mathematics, physics, and computer science students.

Several films have been made from the story, including a feature film in 2007 called Flatland. Other efforts have been short or experimental films, including one narrated by Dudley Moore and a short film with Martin Sheen titled Flatland: The Movie.

Men are portrayed as polygons whose social status is determined by their regularity and the number of their sides with a Circle considered to be the "perfect" shape. On the other hand, females consist only of lines and are required by law to sound a "peace-cry" as they walk, because when a line is coming towards an observer in a 2-D world, her body appears merely as a point. The Square evinces accounts of cases where women have accidentally or deliberately stabbed men to death, as evidence of the need for separate doors for women and men in buildings.

In the world of Flatland, classes are distinguished using the "Art of Hearing," the "Art of Feeling" and the "Art of Sight Recognition." Classes can be distinguished by the sound of one's voice, but the lower classes have more developed vocal organs, enabling them to feign the voice of a polygon or even a circle. Feeling, practised by the lower classes and women, determines the configuration of a person by feeling one of their angles. The "Art of Sight Recognition," practised by the upper classes, is aided by "Fog," which allows an observer to determine the depth of an object. With this, polygons with sharp angles relative to the observer will fade out more rapidly than polygons with more gradual angles. Colour of any kind was banned in Flatland after Isosceles workers painted themselves to impersonate noble Polygons. The Square describes these events, and the ensuing war, at length.

The population of Flatland can "evolve" through the "Law of Nature", which states: "a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon, the son of a Pentagon, a Hexagon; and so on."

This rule is not the case when dealing with isosceles triangles (Soldiers and Workmen) with only two congruent sides. The smallest angle of an isosceles triangle gains thirty arc minutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons. For example, the sons of several hundred-sided polygons will often develop fifty or more sides more than their parents.

An equilateral Triangle is a member of the craftsman class. Squares and Pentagons are the "gentlemen" class, as doctors, lawyers, and other professions. Hexagons are the lowest rank of nobility, all the way up to (near) circles, who make up the priest class. The higher-order polygons have much less of a chance of producing sons, preventing Flatland from being overcrowded with noblemen.

Regular polygons were considered in isolation until chapter seven of the book when the issue of irregularity, or physical deformity, became considered. In a two dimensional world a regular polygon can be identified by a single angle and/or vertex. In order to maintain social cohesion, irregularity is to be abhorred, with moral irregularity and criminality cited, "by some" (in the book), as inevitable additional deformities, a sentiment with which the Square concurs. If the error of deviation is above a stated amount, the irregular polygon faces euthanasia.