The narrator introduces their world, Flatland, to readers who have the privilege of living in Space, using the analogy of an immense sheet of paper. On this surface, geometric figures such as straight lines, triangles, squares, pentagons, and hexagons move freely. These inhabitants are like hard shadows with luminous edges, unable to rise above or sink below the surface of their plane. Although the narrator once viewed this world as the entirety of the universe, their mind has recently opened to a higher conception of reality.
The reader might assume that the inhabitants of Flatland can visually distinguish between the various moving shapes, but this is not the case. The narrator demonstrates this visual limitation by comparing it to looking at a coin or a piece of cardboard on a table. When an observer bends down so that their eye is exactly at the level of the table, the object ceases to appear as a circle or a figure and flattens entirely into a straight line.
This same optical condition applies universally within Flatland. An equilateral triangle, which represents a respectable tradesman in their society, appears as a complete geometric figure only from a bird-eye perspective. When viewed at eye level on the plane, it is reduced entirely to a straight line. Because Flatland lacks a sun or light source to cast clarifying shadows, inhabitants cannot rely on illumination to reveal protruding or receding features. When a shape approaches or retreats, its line simply grows wider or narrower without ever losing its appearance as a straight line.
The narrator acknowledges that this optical limitation raises an obvious question about how individuals manage to recognize and distinguish their friends and acquaintances under such disadvantageous circumstances. However, rather than answering this immediately, the narrator defers the explanation to a later time in order to first discuss the climate and the houses found within their country.