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The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth. Therefore, the horizontal coordinate system is sometimes called the az/el system, [1] the alt/az system, or the alt-azimuth system, among
The word horizontal is derived from the Latin horizon, which derives from the Greek ὁρῐ́ζων, meaning 'separating' or 'marking a boundary'. [2] The word vertical is derived from the late Latin verticalis, which is from the same root as vertex, meaning 'highest point' or more literally the 'turning point' such as in a whirlpool.
The horizontal position has two degrees of freedom, and thus two parameters are sufficient to uniquely describe such a position. However, similarly to the use of Euler angles as a formalism for representing rotations , using only the minimum number of parameters gives singularities , and thus three parameters are required for the horizontal ...
A "vertical" line has undefined or infinite slope (see below). If two points of a road have altitudes y 1 and y 2, the rise is the difference (y 2 − y 1) = Δy. Neglecting the Earth's curvature, if the two points have horizontal distance x 1 and x 2 from a fixed point, the run is (x 2 − x 1) = Δx. The slope between the two points is the ...
This proof is valid only if the line is not horizontal or vertical. [5] Drop a perpendicular from the point P with coordinates (x 0, y 0) to the line with equation Ax + By + C = 0. Label the foot of the perpendicular R. Draw the vertical line through P and label its intersection with the given line S.
A vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). A three-dimensional datum enables the expression of both horizontal and vertical position components in a unified form. [2] The concept can be generalized for other celestial bodies as in planetary datums.
[3] [4] Likewise, for a function of several real variables, a critical point is a value in its domain where the gradient norm is equal to zero (or undefined). [ 5 ] This sort of definition extends to differentiable maps between R m {\displaystyle \mathbb {R} ^{m}} and R n , {\displaystyle \mathbb {R} ^{n},} a critical point ...
Mach bands = visual illusion of brightness (intensive property) Illusions of position (Poggendorff), orientation (Zöllner) and, below, length (Müller-Lyer) Hering Illusion of curvature Delboeuf Illusion of size: left inner circle and right outer circle are actually equal Vertical–horizontal illusion Shifted-chessboard illusion