Rational Trigonometry - Spread

Spread

Spread gives one measure to the 'separation' of two lines (replacing 'angle'): a dimensionless number in the range '0' (parallel) to '1' (perpendicular), which can have several interpretations.


  • Trigonometric: as the sine-ratio for the quadrances in a right triangle (and therefore equivalent to the square of the sine of the angle).
  • Vector: as a rational function of the slopes (or directions) of two lines where they meet.
  • Cartesian: as a rational function of the three co-ordinates used to describe these two vectors.
  • Linear algebra: as a normalized rational function of the square of the determinant of two vectors (from three points) divided by the product of their quadrances.

Read more about this topic:  Rational Trigonometry

Famous quotes containing the word spread:

    “I could have spread my wings and done a thousand things I’ve never done before.”
    —Alan Jay Lerner (1918–1986)

    “To-night she will spread her brown hair on his pillow,
    But I shall be hearing the harsh cries of wild fowl.”
    —Patrick MacDonogh (1902–1961)

    “All catches alight
    At the spread of spring:
    Birds crazed with flight
    Branches that fling
    Leaves up to the light”
    —Philip Larkin (1922–1986)