Geometry
The larger the absolute value of a slope, the steeper the line. A horizontal line has slope 0, a 45° rising line has a slope of +1, and a 45° falling line has a slope of −1. A vertical line's slope is undefined.
The angle θ a line makes with the positive x axis is closely related to the slope m via the tangent function:
and
(see trigonometry).
Two lines are parallel if and only if their slopes are equal and they are not coincident or if they both are vertical and therefore have undefined slopes. Two lines are perpendicular if the product of their slopes is −1 or one has a slope of 0 (a horizontal line) and the other has an undefined slope (a vertical line). Also, another way to determine a perpendicular line is to find the slope of one line and then to get its reciprocal and then reversing its positive or negative sign (e.g. a line perpendicular to a line of slope −2 is +1/2).
Read more about this topic: Slope
Famous quotes containing the word geometry:
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)
“The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematising the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray’s Anatomy.”
—J.G. (James Graham)