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Encyclopedia > Flatland
Title Flatland: A Romance of Many Dimensions

The cover to Flatland, 6th Edition.
Author Edwin Abbott Abbott
Illustrator Edwin Abbott Abbott
Country United Kingdom
Language English
Genre(s) Novella
Publisher Seely & Co.
Released 1884
Media type Print (Hardback)
Pages viii, 100 pp
For various uses of the term Flatlander, see Flatlander (disambiguation)

Flatland: A Romance of Many Dimensions is a 1884 novella by Edwin Abbott Abbott, still popular among mathematics and computer science students, and considered useful reading for people studying topics such as the concept of other dimensions. As a piece of literature, Flatland is respected for its satire on the social hierarchy of Victorian society. Image File history File linksMetadata Download high resolution version (772x1018, 313 KB)The cover to the book, Flatland This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years or... Edwin Abbott Abbott (December 20, 1838 – 1926), English schoolmaster and theologian, is best known as the author of the mathematical satire Flatland (1884). ... Edwin Abbott Abbott (December 20, 1838 – 1926), English schoolmaster and theologian, is best known as the author of the mathematical satire Flatland (1884). ... In political geography and international politics a country is a geographical entity, a territory, most commonly associated with the notions of state or nation. ... The English language is a West Germanic language that originates in England. ... A novella is a narrative work of prose fiction somewhat longer than a short story but shorter than a novel. ... A publisher is a person or entity which engages in the act of publishing. ... This article or section does not cite any references or sources. ... The barcode of an ISBN . ... Flatlander may have one of the following meanings: Flatlanders, a pejorative term for residents of lower altitudes. ... See also: 1883 in literature, other events of 1884, 1885 in literature, list of years in literature. ... Edwin Abbott Abbott (December 20, 1838 – 1926), English schoolmaster and theologian, is best known as the author of the mathematical satire Flatland (1884). ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Computer scaence, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... 2-dimensional renderings (ie. ... Queen Victoria (shown here on the morning of her Ascension to the Throne, 20 June 1837) gave her name to the historic era The Victorian era of the United Kingdom marked the height of the British Industrial Revolution and the apex of the British Empire. ...

Several movies have been made from the story, including two from different directors released in 2007.


The story

The story posits a two dimensional world (Flatland). The narrator, called simply A. Square, a humble square (the social caste of gentlemen and professionals), guides us through some of the implications of life in two dimensions. Part I consists of physical and social descriptions of Flatland. For other uses, see Square. ...

In Part II, Square has a dream about a visit to a one-dimensional world (Lineland), and attempts to convince the realm's ignorant monarch of a second dimension, but finds that it is essentially impossible to make him see outside of his eternally straight line.

The narrator is then visited by a three-dimensional sphere, which he cannot comprehend until he sees the Spaceland for himself (then recognizing his own ignorance (and that of HIS monarch)). This sphere, who remains nameless, is a messiah-like character who visits Flatland at the turn of each millenium to introduce a new apostle to the idea of a third dimension in the hopes of eventually educating the population of Flatland of the existence of Spaceland. From the safety of Spaceland, they are able to observe the leaders of Flatland secretly acknowledging the existence of the sphere and prescribing the silencing of anyone found preaching the truth of Spaceland and the third dimension. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste). Square's brother is among the imprisoned bureaucrats, but the Sphere tells him he can't be saved. A sphere is a perfectly symmetrical geometrical object. ... A bureaucrat is a member of a bureaucracy, usually within an institution of the government. ...

The teacher-student relationship is reversed when, after the Square's mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existance of a fourth (and fifth, and sixth...) spatial dimension. Offended by this presumption and incapable of comprehending a fourth (let alone) infinite dimensions, the Sphere returns his student to Flatand in disgrace.

He then has a dream in which the Sphere visits him again, this time to introduce him to Pointland (which comprises a self-aware point that occupies all space and knows nothing but itself) and learns that he cannot "rescue [the point] from his self-satisfaction". The point (sole inhabitant, monarch, and universe in one) perceives any attempt at communicating with him as simply being a thought originating in his own mind. He is incapable of conceiving the existance of others for his tiny point is his entire universe he can never know anything outside of it and to him it is infintely big anyway. He too is infintely big and fills his entire universe which is essentially himself. He simply sits in solitude congratulating himself for his perfection infintely.

Square recognizes the connection between the ignorance of the monarchs of Pointland and Lineland with his own (and the Sphere's) previous ignorance of the existance of dimensions beyond his own. Square learns to aspire and to teach others to aspire. Given time to cool down, the Sphere has accepted the possibility of infinite dimensions and again wants A. Square to serve as his apostle.

Once returned to Flatland, Square finds it difficult to convince anyone of Spaceland's existence, especially after official decrees are announced - anyone preaching the lies of three diminensions will be imprisoned (or executed, depending on caste). Eventually A. Square himself is imprisoned for just this reason, after telling his entire story at an assembly of a Speculative Society. He is arrested at once and remains in prison at the end of the narrative.

Illustration of a simple house in Flatland.
Illustration of a simple house in Flatland.

Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ...

Social elements

In the book, men are portrayed as polygons whose social class is directly proportional to the number of sides they have; therefore, triangles, having only three sides, are at the bottom of the social ladder and are considered generally unintelligent, while the Priests are composed of multi-sided polygons whose shapes approximate a circle, which is considered to be the "perfect" shape. On the other hand, the female population is comprised only of lines, who are required by law to sway back and forth and sound a "peace-cry" as they walk, due to the fact that when a line is coming towards an observer in a 2-D world, it appears merely as a point. Square talks of accounts where men have been killed (both by accident and on purpose) by being stabbed by women. This explains the need for separate doors for women and men in buildings. Also, colors in Flatland were banned, when lower classes painted themselves to appear to be higher ordered (i.e. women tried to be circles). A polygon (from the Greek poly, for many, and gonos, for angle) is a closed planar path composed of a finite number of sequential straight line segments. ... This article is about proportionality, the mathematical relation. ... A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ... Circle illustration This article is about the shape and mathematical concept of circle. ... In geometry a digon is a polygon with two sides and two vertices. ... A spatial point is an entity with a location in space but no extent (volume, area or length). ...

In the world of Flatland, classes are distinguished using the "Art of Feeling" and the "Art of Sight Recognition". 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. 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), for their evolution occurs through eventually achieving the status of an equilateral triangle, removing them from serfdom. The smallest angle of an isosceles triangle gains thirty minutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons; the sons of several hundred-sided polygons will often develop fifty or more sides than their parents. For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... Costumes of slaves or serfs, from the sixth to the twelfth centuries, collected by H. de Vielcastel from original documents in European libraries. ...

In the book, the three-dimensional Sphere has the ability to stand inches away from a Flatlander and observe them without being seen, can remove Flatland objects from closed containers and teleport them via the third dimension without traversing the space in between, and is capable of seeing and touching the inside and outside of everything in the two dimensional universe; at one point, the Sphere gently pokes the narrator's intestines and launches him into three dimensions as proof of his powers. A sphere is a perfectly symmetrical geometrical object. ... Teleportation is the movement of objects or elementary particles from one place to another, more or less instantaneously, without traveling through space. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... The intestine is the portion of the alimentary canal extending from the stomach to the anus and, in humans and other mammals, consists of two segments, the small intestine and the large intestine. ...

Editions in print

  • Flatland (5th edition, 1963), 1983 reprint with foreword by Isaac Asimov, HarperCollins, ISBN 0-06-463573-2
    • bound together with Dionys Burger's Sphereland (1994), HarperCollins, ISBN 0-06-273276-5
  • The Annotated Flatland (2002), coauthor Ian Stewart, Perseus Publishing, ISBN 0-73820541-9
  • Oxford University Press (2006), ISBN 0-19-280598-3
  • Dover Publications thrift edition (2007), ISBN 0-486-27263-X

Isaac Asimov (January 2?, 1920? – April 6, 1992, IPA: , originally Исаак Озимов but now transcribed into Russian as Айзек Азимов) was a Russian-born American author and professor of biochemistry, a highly successful and exceptionally prolific writer best known for his works of science fiction and for his popular science books. ... Sphereland is a 1965 novel by Dionys Burger, and is a sequel to Flatland, a novel by A. Square (A pen name of Edwin Abbott Abbott). ...

Related works


Numerous companions to Flatland have been written, including:

Short stories inspired by Flatland include: Charles Howard Hinton (1853-1907) was a British mathematician and writer of science fiction works that he called scientific romances. ... 1907 (MCMVII) was a common year starting on Tuesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 13-day-slower Julian calendar). ... Sphereland is a 1965 novel by Dionys Burger, and is a sequel to Flatland, a novel by A. Square (A pen name of Edwin Abbott Abbott). ... The Planiverse (ISBN 0387989161) is a book by A. K. Dewdney, written in 1984. ... Alexander Keewatin Dewdney (* August 5, 1941 in London, Ontario) is a Canadian mathematician, computer scientist, and philosopher who has written a number of books on the future and implications of modern computing. ... Flatterland is a 2001 book by mathematician and science popularizer Ian Stewart about non-Euclidean geometry. ... Ian Stewart, FRS (b. ... Cover of Rudy Ruckers Novel, Spaceland. ... Rudy Rucker, Fall 2004, photo by Georgia Rucker. ...

  • The Incredible Umbrella by Marvin Kaye (1980) includes a chapter set in Flatland
  • Message Found in a Copy of "Flatland" by Rudy Rucker (1983)
  • Tangents by Greg Bear

Marvin Kaye is an American mystery, fantasy, and horror author and editor. ... Rudy Rucker, Fall 2004, photo by Georgia Rucker. ... Gregory Dale Bear (born August 20, 1951) is a science fiction author. ...


  • Flatland the Film (2007)], a 95-minute animated independent version directed by Ladd Ehlinger Jr. Available on DVD; not released theatrically.[1] Updates setting to contemporary North America rather than Victorian England (e.g. with a "president" instead of a "king").[2]
  • Flatland: the Movie, a 30-minute animated educational film with Michael York and Charlie Sheen among the voice actors, slated to be released in 2007 [3]
  • Flatland, A 1982 short film directed by mathematician Michele Emmer. [1]
  • Flatland, A 1965 animated film directed by Eric Martin and narrated by Dudley Moore.

Other movie relationships: Michael York (born March 27, 1942, Fulmer, England) is a prolific actor now resident in California. ... Charles Irwin Sheen (born Carlos Irwin Estévez on September 3, 1965) is a Golden Globe Award-winning and Emmy-nominated American actor. ... Dudley Stuart John Moore, CBE (April 19, 1935 – March 27, 2002), was an Academy-Award nominated British comedian, actor and musician. ...

  • An animated sequence in the movie What the Bleep Do We Know!? shows a human interacting with a Flatlander.
  • A 1997 animated short Flatworld is unrelated to Flatland.

What the Bleep Do We Know!? (also written What tнē #$*! Ďө ωΣ (k)πow!? and What the #$*! Do We Know!?) is a controversial 2004 film that combines documentary interviews and a fictional narrative to posit a connection between science and spirituality based upon the Ramthas School of Enlightenment of JZ Knight...


  • "Homer3," the third segment of the 29 October 1995 episode of The Simpsons, portrays an inhabitant of a two-dimensional universe entering the third dimension.
  • In an episode of Cosmos, Carl Sagan discusses Flatland as an analogy to explain other dimensions other than our three physical dimensions.

Treehouse of Horror VI is the sixth episode of The Simpsons seventh season, as well as the sixth Halloween episode. ... Simpsons redirects here. ... Cosmos: A Personal Voyage was the name of a thirteen part television series produced by Carl Sagan and Ann Druyan which was first broadcast by the Public Broadcasting Service in 1980. ... Insert non-formatted text here Carl Edward Sagan (November 9, 1934 – December 20, 1996) was an American astronomer and astrobiologist and a highly successful popularizer of astronomy, astrophysics, and other natural sciences. ...


Role-playing games based on Flatland include:

  • "KaSE Edwin A Abbot’s Flatland (Inflated)" by T Craig Drake, Red Anvil Productions (2005)
  • "The Flatland Role Playing Game" by Marcus Rowland (1998), revised and expanded as "The Original Flatland Role Playing Game" (2006).

Marcus Rowland is a laboratory technician and the author of the Forgotten Futures and Diana: Warrior Princess role-playing games, and various scenarios for other RPGs. ...

Other uses

  • Christian teacher Rob Bell borrowed the "flatland" concept in his Everything is Spiritual tour.
  • Christian author David Brandt Berg also used the "flatland" concept in one of his lectures on the existence of the spirit world, published in Dare to be Different.
  • Lisa Randall, a theoretical physicist, gave a brief overview of Flatland in her book Warped Passages.
  • Independent hip-hop musician, proGrammar, penned the following lyrics in his song, "Music": "Flatlanders can't understand the measure of a man from a different planet, with a different plan."

This article or section does not cite any references or sources. ... Lisa Randall at Harvard University Lisa Randall (born 18 June 1962) is a well-known American particle physicist, and the most cited high-energy physicist in the period 1999 to 2004. ... Warped Passages is a book about particle physics in general and additional dimensions of space in particular by Lisa Randall, published in 2005. ... Hip hop (also spelled hip-hop or hiphop) is both a music genre and a cultural movement developed in urban communities starting in the 1970s, predominantly by African Americans. ...


  1. ^ Flatland the Film. Retrieved on 2007-01-14.
  2. ^ Flatland the Film. Retrieved on 2007-05-18.
  3. ^ Flatland the Movie. Retrieved on 2006-06-22.

2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era. ... January 14 is the 14th day of the year in the Gregorian calendar. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era. ... May 18 is the 138th day of the year (139th in leap years) in the Gregorian calendar. ... For the Manfred Mann album, see 2006 (album). ... June 22 is the 173rd day of the year (174th in leap years) in the Gregorian calendar. ...


  • Tuck, Donald H. (1974). The Encyclopedia of Science Fiction and Fantasy. Chicago: Advent, 1. ISBN 0-911682-20-1. 

Author of A Handbook of Science Fiction and Fantasy. ...

External links

Wikisource has original text related to this article:

Image File history File links Wikisource-logo. ... The original Wikisource logo. ...

Online versions of the text

Project Gutenberg, abbreviated as PG, is a volunteer effort to digitize, archive, and distribute cultural works. ... Project Gutenberg, abbreviated as PG, is a volunteer effort to digitize, archive, and distribute cultural works. ... HTML, short for Hypertext Markup Language, is the predominant markup language for the creation of web pages. ... PDF is an abbreviation with several meanings: Portable Document Format Post-doctoral fellowship Probability density function There also is an electronic design automation company named PDF Solutions. ...


  Results from FactBites:
Flatland BMX - Wikipedia, the free encyclopedia (816 words)
Flatland is BMX riding that is mostly performed on smooth flat surfaces, with flatland specific frames, front and rear bolt on axle pegs, and a hollow front stem to facilitate the bars being able to rotate endlessy without tangling the brake cable.
When flatland riding first came into being, most riders would do one trick, and then get back to the pedals and that was it, but by combining different body, and bicycle positions, into "combos" and "linking" them together, riders challenge themselves further by doing several tricks in a row without stopping inbetween each move.
Flatland riding is usually a combination of many different kinds of moves, often linked together in a non-stop fashion as the rider goes through as few as 2 or 3, or as many as 10-12 moves, and position or direction changes in a row, and then finally returning their feet to the pedals.
Flatland (2131 words)
But Flatland is still unready to cope with concepts such as the curvature or expansion of space.
Whereas in Flatland the inhabitants are polygonal shapes sliding about on an idealized tabletop world, in The Planiverse the denizens walk on the one-dimensional surface of a circular planet (much like Hinton's Astrians), must climb over one another to pass, and build complex machines of springs and hinges.
Whereas Flatland, boiled down to the core, teaches the single lesson that other dimensions are conceivable as mathematical constructs, Sphereland introduces the notions of curved and expanding space and how they apply to the real world.
  More results at FactBites »



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