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Scale height. The earth atmosphere's scale height is about 8.5 km, as can be confirmed from this diagram of air pressure p by altitude h: At an altitude of 0, 8.5, and 17 km, the pressure is about 1000, 370, and 140 hPa, respectively. In atmospheric, earth, and planetary sciences, a scale height, usually denoted by the capital letter H, is a ...
Instead, assuming constant temperature, integrating gives the second barometric formula: = / In this formulation, R * is the gas constant, and the term R * T/Mg gives the scale height (approximately equal to 8.4 km for the troposphere).
In affine geometry, uniform scaling (or isotropic scaling[1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically). The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so ...
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations. Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
This implies that the vertical scale factor, h, equals the horizontal scale factor, k. Since k = sec φ, so must h. The graph shows the variation of this scale factor with latitude. Some numerical values are listed below. at latitude 30° the scale factor is k = sec 30° = 1.15, at latitude 45° the scale factor is k = sec 45° = 1.41,
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape.
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 ...
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry , height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers .