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Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Plot Summary

See Plot Diagram


Part 1: This World

Flatland is narrated by A Square, a two-dimensional geometric figure. In the first part of the book, A Square introduces readers to Flatland and its inhabitants. The people of Flatland see each other as a series of lines. They infer shape by relative haziness in their vision or by touching angles. The society of Flatland is divided into rigid classes based on the number of sides a figure possesses, which is also assumed to correlate to intellect and moral character. Figures accrue sides generationally, with the son of most figures having one more side than his father. The leaders of the society are circular priest kings. Women are straight lines and assumed to have no capacity for higher thought. Laws and customs restrict their movement through the threat of death. Figures with irregular angles are considered deficient, criminal, and dangerous to society. A Square also talks about the historical episode in which color threatened to overturn the entire hierarchy. This revolt was brutally suppressed by the ruling class of Circles, and color was outlawed.

Part 2: Other Worlds

Part 2 deals with A Square's journeys to realms with different numbers of dimensions. He dreams that he travels to a realm made of a single straight line and converses with its king. A Square believes he is explaining his world of two dimensions clearly, but the King of Lineland, for whom men are lines and women are single points and to whom all other people appear as a single dot, cannot understand. Furthermore, nothing A Square does can convince him. The King, frustrated with A Square's claims, commands his subjects to attack.

The next night, A Square is visited by Sphere, who comes to Flatland to share the Gospel of Three Dimensions. As he tries to explain solid space, Sphere moves through Flatland, visible as an expanding and contracting circle. He describes dimensions through geometric progression and pure math. He moves things from inside locked cabinets and presses on A Square's interior to try to demonstrate that he is above the space. Ultimately, A Square does not believe him until Sphere pulls him out of Flatland altogether and shows him Flatland from above. A Square then worships Sphere as a wise, divine teacher. Sphere shows A Square the council chambers where a measure is drafted to suppress knowledge of the third dimension. Sphere manifests in the chambers, and the council arrests A Square's brother for witnessing it. Sphere then introduces an awed A Square to a Cube, and A Square asks Sphere to show him the fourth dimension. Sphere becomes angry, saying there is no such thing. He returns A Square to Flatland.

A Square then has another vision in which he and Sphere visit a world made of a single point that thinks it is the whole universe. Neither can convince the egotistical little being that other people even exist, foreshadowing the difficulty A Square will have convincing anyone of the third dimension. However, he does try to convince people with reason, despite the legal prohibition, until in frustration he tells his entire story and is thrown into prison. His prison memoirs are the book, Flatland.

Flatland Plot Diagram

Falling ActionRising ActionResolutionClimax123456789101112Introduction


1 A Square introduces readers to Flatland and its politics.

Rising Action

2 A Square has a vision of Lineland.

3 The King of Lineland says there is no second dimension.

4 Sphere manifests in Flatland but cannot convert A Square.

5 Sphere pulls A Square into Spaceland.

6 The Circles prohibit discussion of three dimensions.

7 Sphere shows A Square a cube and encourages him to feel it.

8 A Square asks Sphere about fourth dimension, angering him.


9 A Square envisions the ignorance of Pointland.

Falling Action

10 A Square tries to use pure reason to share his message.

11 A Square tells his whole story and is imprisoned.


12 From prison, A Square writes Flatland.

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