Flatland: The Movie is a short animated film which was released to video in 2007. The cast includes the voices of actors Martin Sheen, Kristen Bell and Tony Hale. The story is based on the 1884 science fiction novella Flatland: A Romance of Many Dimensions written by Edwin A. Abbott.
Plot
The 2-dimensional Arthur Square awakens from a dream of strange, glowing symbols. He lives with his wife, Arlene Square, and his curious granddaughter Hex, a hexagon. Hex and Arthur discuss the laws of inheritance: how each new generation of Flatlanders, beginning with triangles, gains a new side until the shapes become indistinguishable from circles. They also discuss how a citizen's shape affects their job, with triangles performing menial labor and circles ruling Flatland in the priest class. They witness a cruel incident where a Circle Priest arrests a slightly irregular octagon child, prompting Hex to yet again wonder what happened to her pentagonal parents. Arthur tells her that he will tell her someday.
The head circle ruler of Flatland, Pantocyclus, issues a new edict that bans discussion of heretical topics such as a third dimension or the ruins at Area 33H. Arthur recognizes an image of the ruins from his dream.
Arthur gives Hex a geometry lesson, showing how powers in arithmetic can be translated to geometrical dimensions. When Hex speculates on a third dimension, Arthur becomes infuriated and sends her to her room. To calm Hex, Arlene gives her her mother's box containing books and a model of the symbols at Area 33H.
That night, Arthur Square is taken to a strange landscape. He encounters the insane King of Pointland, a being of zero dimensions. Then he encounters Lineland, a universe of one dimension that is populated by an arrogant line segment King who cannot imagine a new dimension that he cannot see. Finally, Arthur is whisked back to his living room. He hears a voice booming out and sees a point grow to a circle and then back to a point. The being identifies himself as Spherius, a three-dimensional solid from Spaceland. After Spherius fails to explain the third dimension, Arthur is popped into Spaceland. They stop at Area 33H and Arthur realizes that the symbols show a progression from point to line to square to cube, and that the constantly changing shape in the center is actually a cube, halfway through the plane of Flatland and spinning along all three axes. Arthur asks Spherius to show him the fourth dimension and the fifth dimension, but Spherius says there couldn't possibly be a higher dimension. He tells Arthur to spread the word of the third dimension and drops Arthur back into bed. Meanwhile, at the Ministry, Pantocyclus is ordering the triangle-guards and circles, including Miss Helios (Arthur's boss), to beware any employees who mention the third dimension and to guard Area 33H.
Hex leaves to explore Area 33H, but a triangle guard spots her. At the Ministry, Arthur is talking to his brother, when an alarm goes off. Over the intercom, Miss Helios orders all guards to catch an intruder at Area 33H. Arthur realizes it might be Hex and persuades Abbott (his brother) to help him steal a Ministry car.
Abbott and Arthur arrive at the ruins moments before the triangle guards. With Abbott distracting the guards, Arthur goes to the symbols and finds Hex terrified. Arthur admits to her that her parents were arrested and killed for their theories about the third dimension. With the guards closing in, Arthur pushes Hex into the cube symbol, which pops her up into the third dimension. Arthur is arrested by Miss Helios.
Arthur is hastily brought into a courtroom with Pantocyclus proceeding over his trial for heresy. Arlene arrives and asks where Hex is. In his cell, Arthur assures her that Hex escaped 'upward' into the third dimension and is safe. A nearby pentagon begins broadcasting the trial. Pantocyclus challenges Arthur to show everyone the third dimension Arthur admits that he can't but pleads to his fellow Flatlanders that reason dictates a third dimension. He challenges them to aspire to be greater than their shapes, angering the Circles immensely. In a fit of rage, Pantocyclus sentences Arthur to death, but Spherius suddenly pops Arthur out of Flatland.