Where does turn collide?

In differential geometry, the turning number (rotation index) of a closed plane curve is the net number of complete rotations made by its tangent vector as the curve is traversed once. do Carmo's Differential Geometry of Curves and Surfaces presents the theorem of turning tangents, which fixes this number as plus or minus one for a simple closed curve. The referent is an integer invariant of a curve, sharing only the word with a musical figure or a literary pivot.[1]

Unit

The signed integer count of full tangent rotations around a closed curve

Recovery means

Not applicable

Measured by

Computed as the total signed change in tangent angle divided by 2π as the curve is traversed

In poetics, the turn (Italian volta) is the point where a poem shifts its thought, feeling, or argument, classically the move from problem to resolution between the octave and sestet of a sonnet. The Princeton Encyclopedia of Poetry and Poetics treats the volta as a structural pivot central to how many lyric forms make meaning. The referent is a conceptual turning point in a text, unrelated to a melodic ornament or a geometric rotation count despite the shared word.[2]

Unit

The structural point at which a poem reverses or redirects its argument

Recovery means

Not applicable

Measured by

Located by analysing where the poem's rhetoric, syntax, or form shifts direction