The first half of the novella is a description of this two-dimensional world, such as how it looks and how the figures move, with a clever analysis of Flatland’s social hierarchy, which is dictated by the number of sides someone has. Square's subsequent explorations lead him to Lineland (a one-dimensional world), Pointland (no dimensions), and then to Spaceland with its three dimensions.
The novella is narrated by one of Flatland's residents, A. Square. Flatland is very old Hard Science Fiction, if you look at it right. It's clever, funny, and sad. It includes a well-fleshed-out alien society with similarities to our own, several different alternate universes, genetics, politics, religion, slavery, war, rebellion, imprisonment, madness, and death. And math. And geometry. And some rather clever puns. Women are simple line-segments, while men are regular polygons with various numbers of sides. The narrator is a humble square, a member of the social caste of gentlemen and professionals in a society of geometric figures, who guides us through some of the implications of life in two dimensions. The Square has a dream about a visit to a one-dimensional world (Lineland) which is inhabited by "lustrous points". He 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.
He is then visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland for himself. This Sphere visits Flatland at the turn of each millennium 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.
After the Square's