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Geomathematics (also: mathematical geosciences, mathematical geology, mathematical geophysics) is the application of mathematical methods to solve problems in geosciences, including geology and geophysics, and particularly geodynamics and seismology.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length.. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude.
This formula only works because of the mathematical fact that the gravity of a uniform spherical body, as measured on or above its surface, is the same as if all its mass were concentrated at a point at its centre. This is what allows us to use the Earth's radius for r. The value obtained agrees approximately with the measured value of g.
This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d (or any one side) approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.
The Universal Soil Loss Equation (USLE) is a widely used mathematical model that describes soil erosion processes. [1]Erosion models play critical roles in soil and water resource conservation and nonpoint source pollution assessments, including: sediment load assessment and inventory, conservation planning and design for sediment control, and for the advancement of scientific understanding.
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
The transport formula of Meyer-Peter and Müller, originally developed in 1948, [25] was designed for well-sorted fine gravel at a transport stage of about 8. [19] The formula uses the above nondimensionalization for shear stress, [19] = () (),
The continuity equation is a mathematical version of stating that the geologic object or medium is continuous, which means no empty space can be found in the object. [17] This equation is commonly used in numerical modeling in geology. [17] One example is the continuity equation of mass of fluid.