This is the annotated and summarized version of this book. This summarized version consists of 18000 words in approxamte.
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The story describes a two-dimensional world occupied by geometric figures, where women are simple line segments, while men are polygons with various numbers of sides. The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium. On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points". These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so. In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. Following this vision, he is visited by a three-dimensional sphere. Similar to the "points" in Lineland, the Square is unable to see the sphere as anything other than a circle. The Sphere then levitates up and down through the Flatland, allowing Square to see the circle expand and retract. The Square is not fully convinced until he sees Spaceland (a tridimensional world) 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 hope of eventually educating the population of Flatland. 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), including A Square's brother, B. After Square's mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth and higher spatial dimension; but the Sphere returns his student to Flatland in disgrace. The Square then has a dream in which the Sphere visits him again, this time to introduce him to Portland, whereof the point (sole inhabitant, monarch, and the universe in one) perceives any communication as a thought originating in his own mind (cf. Solipsism): "You see," said my Teacher, "how little your words have done. So far as the Monarch understands them at all, he accepts them as his own – for he cannot conceive of any other except himself – and plumes himself upon the variety of Its Thought as an instance of creative Power. Let us leave this God of Portland to the ignorant fruition of his omnipresence and omniscience: nothing that you or I can do can rescue him from his self-satisfaction." — the Sphere
