Line of greatest slope
Encyclopedia
In topography
, the line of greatest slope is a curve following the steepest slope
. It is always orthogonal to the contour line
s. Mathematically it is determined by the gradient
of the height, taken as a potential field, so the lines of greatest slope are the analogon of lines of force
.
If inertial forces and terrain roughness are set side, a ball rolling down a slope, or water flowing down, will follow the line of greatest slope.
Topography
Topography is the study of Earth's surface shape and features or those ofplanets, moons, and asteroids...
, the line of greatest slope is a curve following the steepest slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
. It is always orthogonal to the contour line
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...
s. Mathematically it is determined by the gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
of the height, taken as a potential field, so the lines of greatest slope are the analogon of lines of force
Line of force
A line of force in Faraday's extended sense is synonymous with Maxwell's line of induction. According to J.J. Thomson, Faraday usually discusses lines of force as chains of polarized particles in a dielectric, yet sometimes Faraday discusses them as having an existence all their own as in...
.
If inertial forces and terrain roughness are set side, a ball rolling down a slope, or water flowing down, will follow the line of greatest slope.