linclinaison

Linclinaison is a term used to describe the angle of tilt of a line, a plane, or an object relative to a reference plane or axis. The concept appears across geometry, astronomy, surveying, and engineering, with definitions and conventions that depend on the context.

In geometry, the inclination of a line in a two-dimensional plane is the angle between the line and the positive x-axis. If a line has a direction vector (dx, dy), its inclination α is given by α = arctan2(dy, dx) (in degrees or radians). The slope is m = tan α.

For a plane, inclination refers to the tilt relative to the horizontal plane. A plane described by ax + by + cz + d = 0 has normal vector n = (a, b, c). The angle between the plane and the horizontal plane is φ = arccos(|c| / sqrt(a^2 + b^2 + c^2)), and equivalently tan φ = sqrt(a^2 + b^2) / |c|. This measures how steeply the plane rises from the horizontal.

In astronomy, the orbital inclination i is the angle between the orbital plane and a reference plane (typically the ecliptic or the celestial equator). It ranges from 0 to 180 degrees. An orbit with i = 0 lies in the reference plane, while i = 90 degrees indicates a polar orbit. Inclination is one of the classical orbital elements that determine an orbit’s orientation and visibility from a given observer.

Measurement and applications: Clinometers and inclinometers measure tilt in surveying, engineering, aviation, and geoscience. Inclination informs road and rail design, satellite tracking, and the interpretation of geological layer orientation.