Metropolis is the capital of Flatland, seen by Square from a vantage point that makes the city’s ordered surface transparent and brings its hidden interiors into view. Its monumental Assembly Hall becomes the stage for a recurring political ritual: at the opening of the year 2000, the Council confronts Sphere’s announcement of Three-Dimensional space, while its own records expose a long-standing policy of suppressing revelations from another world.

Setting and View from Above

As Sphere guides Square across Flatland, the city first appears as an immense Polygonal structure, surrounded by dense rows of Pentagonal buildings intersecting at right angles. From this elevated perspective, the recognizable streets and civic center belong to a landscape that can be read as a pattern, but the view soon exceeds the city’s visible surface. The farther the travelers recede, the larger their field of vision becomes; Square sees the interiors of houses and the creatures within them, then the depths of mines and the innermost caverns of hills. Metropolis thus marks a change in access as well as a place: from above, boundaries that govern ordinary vision cease to conceal what lies inside or below.

The Millennial Council

Sphere and Square descend near the Assembly Hall on the first hour of the first day of the year 2000. The highest Circles are meeting in solemn conclave, following the precedent of assemblies held at the opening of the years 1000 and 0. The meeting’s formality gives the city’s central institution a history measured in millennia, and makes the current gathering part of a repeated state response rather than an isolated debate.

The minutes are read by Square’s brother, a perfectly Symmetrical Square serving as Chief Clerk of the High Council. The records state that earlier councils had faced people claiming revelations from another world and demonstrations that had driven themselves and others into frenzy. In response, the Grand Council had ordered the Prefects to search for such people at every millennial opening and to punish or detain them according to their geometric rank: Isosceles were to be destroyed, regular Triangles scourged and imprisoned, Squares and Pentagons sent to the district Asylum, and those of higher rank arrested and brought to the capital for judgment. The Assembly Hall therefore stands at the center of both government and an established system for containing challenges to its account of reality.

Sphere’s Appearance and Its Suppression

As the Council passes the resolution for a third time, Sphere tells Square that the apostle of the Gospel of Three Dimensions faces death or imprisonment. Square, newly convinced of the reality of higher-dimensional space, wants to descend and enlighten the Council himself, but Sphere tells him to remain where he is and proceeds into the gathering. He announces that a land of Three Dimensions exists.

The younger Counsellors recoil as Sphere’s circular section widens before them. At a signal from the presiding Circle, six low-ranking Isosceles rush from different quarters; their cries alternate between claiming to have caught Sphere and realizing that he is going and gone. The presiding Circle, however, shows no surprise. He explains to the junior Circles that secret archives accessible only to him record similar events at the two previous millennial openings, and orders them to say nothing outside the Cabinet. The attempted revelation is thus met by a revealing institutional response: the Council has encountered Sphere before, but has kept those encounters secret.

Meaning Within Flatland’s Spatial Order

The approach to Metropolis links changes in physical viewpoint to unequal access to knowledge. On the surface, the Assembly Hall and its surrounding streets form a legible civic landscape; from higher space, Square can see through buildings and into the earth. At the Council, the same distinction becomes political: a claim that cannot be accommodated within Flatland’s familiar dimensions is treated as a threat, and the records of prior encounters are confined to secret archives.

Metropolis consequently joins the book’s demonstration of dimensional perception to its account of authority. Its Council can organize searches and punishments across Flatland, yet its own proceedings repeat an effort to contain what Sphere’s appearance makes visible. The city’s elevated view opens the world; its central chamber tries to close the knowledge that view implies.