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 have spread my dreams under your feet;
Tread softly because you tread on my dreams.”
—William Butler Yeats (1865–1939)
“There’s Margaret and Marjorie and Dorothy and Nan,
A Daphne and a Mary who live in privacy;
One’s had her fill of lovers, another’s had but one,
Another boasts, “I pick and choose and have but two or three.”
If head and limb have beauty and the instep’s high and light
They can spread out what sail they please for all I have to say....”
—William Butler Yeats (1865–1939)
“Cows sometimes wear an expression resembling wonderment arrested on its way to becoming a question. In the eye of superior intelligence, on the other hand, lies the nil admirari spread out like the monotony of a cloudless sky.”
—Friedrich Nietzsche (1844–1900)