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A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. [1][2] It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of ...
Angular distance. Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere. When the rays are lines of sight from an observer to two points in space, it is known as the ...
The angle we seek to maximize is β − α. The tangent of the angle increases as the angle increases; therefore it suffices to maximize. Since b − a is a positive constant, we only need to maximize the fraction that follows it. Differentiating, we get. Therefore the angle increases as x goes from 0 to √ab and decreases as x increases from ...
Topographic maps display elevation above ground and are complementary to bathymetric charts. Bathymeric charts showcase depth using a series of lines and points at equal intervals, called depth contours or isobaths (a type of contour line). A closed shape with increasingly smaller shapes inside of it can indicate an ocean trench or a seamount ...
A cross-section view of a compression seal. In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher- dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space ...
This is the convention followed in this article. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distance r along the radial line connecting the point to the fixed point of origin; the polar angle θ ...
A stereoplotter uses stereo photographs to determine elevations. It has been the primary method to plot contour lines on topographic maps since the 1930s. Although the specific devices have advanced technologically, they are all based on the apparent change in position of a feature in the two stereo photographs.
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.