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:
“In a moment when criticism shows a singular dearth of direction every man has to be a law unto himself in matters of theatre, writing, and painting. While the American Mercury and the new Ford continue to spread a thin varnish of Ritz over the whole United States there is a certain virtue in being unfashionable.”
—John Dos Passos (1896–1970)
“When I married Humphrey I made up my mind to like sermons, and I set out by liking the end very much. That soon spread to the middle and the beginning, because I couldn’t have the end without them.”
—George Eliot [Mary Ann (or Marian)
“We have seen when the earth had to be prepared for the habitation of man, a veil, as it were, of intermediate being was spread between him and its darkness, in which were joined in a subdued measure, the stability and insensibilty of the earth, and the passion and perishing of mankind.”
—John Ruskin (1819–1900)