Plane (Geometric Concept)

First Appearance and Context

The term is defined in The Dictionary (Fourth Edition, A.R. 3000) with multiple senses. In displays about the Hylaean Way, classical scenes of Ethras depict a flat open area in the Periklyne called “the Plane,” where figures draw proofs and conduct public dialogs; that place‑name is a separate usage from the geometric concept covered here.

Roles/Actions and Affiliations

Within Diaxan theorics and the mathic tradition, the plane is one of the basic ideal objects studied by Theors. It is invoked when reasoning about shape, measurement, and idealized constructions, distinct from any imperfect drawings in the physical world.

Relationships

The concept belongs to the family of pure geometrical objects (such as lines and triangles) treated as elements of a higher, ideal domain glimpsed in the foundational story of Cnous. The word “Plane” also names a famed expanse within the Periklyne at Ethras used for proofs and debate; that usage is historical and topographical, not geometric.

Descriptions/Characteristics

The Dictionary glosses the geometric sense as a two‑dimensional manifold in three‑dimensional space having a flat metric, and extends the meaning to analogous manifolds in higher‑dimensional spaces. In practice, it functions as an ideal setting for figures, measurements, and theorems, independent of the imperfections of any drawn surface.

Current Status/Location

The plane remains a standard item of theorical vocabulary and is defined in reference works in use among avout. The Dictionary further notes non‑geometric senses: a proper name for a venue of public dialog and a verb meaning to devastate an interlocutor’s position during a dialog; neither of those senses is the subject of this page.