anglewhether

Anglewhether is a term used in geometry and related fields to denote a conditional angular measure. It expresses the idea that the angle between two lines or vectors depends on a boolean predicate. The concept is informal and appears in problem sets and algorithm descriptions rather than as a formal mathematical object. The term suggests that the angle can be either the standard angle or its supplement, according to a condition.

Definition: Let L1 and L2 be lines through a common vertex, and let θ be the conventional angle between them (0 ≤ θ ≤ 180 degrees). For a boolean predicate p, the anglewhether θ_w is defined as θ if p is true, and as 180° − θ if p is false. Equivalently, θ_w equals θ when p is true, else its supplementary angle. In vector form, if v1 and v2 have an angle θ, then anglewhether is θ when p is true, and 180° − θ when p is false.

Extensions: In higher dimensions, anglewhether can refer to the conditional angle between vectors or subspaces with the choice determined by p. The notion accommodates problems where orientation or which angle is relevant depends on a separate binary condition.

Applications: The concept is used mainly as a modeling device in problem solving, computational geometry, and robotics to encode decisions about choosing an acute or obtuse angle based on a rule. It helps formalize conditional angular constraints within a single symbol rather than switching between cases.

Example: Two lines intersecting with θ = 60 degrees. If p is true, anglewhether is 60 degrees; if p is false, anglewhether is 120 degrees.

See also: angle, supplementary angle, orientation, boolean, conditional logic.