Planeedilt

Planeedilt is a fictional geometric concept used in speculative fiction and thought experiments. It is designed to quantify the tilt of a planar section relative to a fixed reference direction.

In three-dimensional space, let a plane have unit normal vector n and let the reference direction be a unit vector k representing the "up" direction. The planeedilt θ is defined as arccos(|n · k|). This yields θ in the interval [0, π/2], where θ = 0 indicates the plane is horizontal (parallel to the reference plane) and larger values indicate a steeper tilt. The absolute value ensures the measure depends only on the magnitude of tilt, not the orientation around the normal.

The concept generalizes to higher dimensions by measuring the angle between a given plane and a fixed reference hyperplane along a chosen normal direction. In all cases, planeedilt is intended as a tilt magnitude common to both mathematical analogies and world-building descriptions.

Origin and usage: The term is said to have been coined in fictional contexts by writers exploring orientation and gravity in invented worlds. It is not part of standard mathematical vocabulary, and outside fiction its usage is limited. When used, it functions as a shorthand for discussing how much a plane deviates from a reference orientation.

It is related to standard concepts such as the angle between planes and dihedral angle.