![]() ![]() From the safety of Spaceland, they can oversee the leaders of Flatland, acknowledging the Sphere's existence and prescribing the silencing. 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. Still unable to comprehend 3D, the Sphere takes the Square to the third dimension, Spaceland. The Square is still unable to comprehend the third dimension, so the Sphere resorts to deeds: he gives info about the "insides" of the house, moves a cup through the third dimension, and even goes inside the Square for a bit. ![]() The Sphere then tries further to convince the Square of the third dimension by dimensional analogies (a point becomes a line, a line becomes a square). The Sphere then levitates up and down through Flatland, allowing the Square to see the circle expand and contract between great circle and small circles. Similar to the "points" in Lineland, he is unable to see the three-dimensional object as anything other than a circle (more precisely, a disk). In the end, the monarch of Lineland tries to kill the Square rather than tolerate him any further.įollowing this vision, the Square is visited by a sphere. Thus, the Square attempts to convince the realm's monarch of a second dimension but cannot do so. ![]() These points and lines are unable to see the Square as anything other than a set of points on a line. On New Year's Eve, the Square dreams of a visit to a one-dimensional world, “Lineland”, inhabited by men, consisting of lines, while the women consisted of "lustrous points". 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. 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 story describes a two-dimensional world inhabited by geometric figures women are line segments, while men are polygons with various numbers of sides. Illustration of a simple house in Flatland. ![]()
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