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:
“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)
“I could have spread my wings and done a thousand things I’ve never done before.”
—Alan Jay Lerner (1918–1986)
“The philanthropist too often surrounds mankind with the remembrance of his own cast- off griefs as an atmosphere, and calls it sympathy. We should impart our courage, and not our despair, our health and ease, and not our disease, and take care that this does not spread by contagion.”
—Henry David Thoreau (1817–1862)