the science of the graphic representation of the shape of deposits and properties (features) of minerals in the earth’s interior, methods of calculating and keeping track of changes in reserves, and methods of solving geometric problems related to carrying on mining work. Questions of mining geometry were formerly studied in various courses in the fields of geological analysis, mine surveying, and mining science. In the 1920’s mining geometry became an independent discipline.
A mineral Deposit Is usually a complex body in shape and structure. Using limited data on a deposit, obtained during an analysis of its value, it is necessary to reproduce the most probable shape of the deposit, determine the mineral’s conditions of occurrence among other rocks, and also study the distribution of the mineral’s properties that are important for production. In developing methods that make it possible to solve these problems, mining geometry uses the ordinary methods of geometry, mathematical statistics, and probability theory. There are two large groups among the various shapes of deposits: beds or bedlike deposits and deposits of irregular shape. There are some differences between the mining geometry problems solved in reference to these two groups of deposits. In mining geometry the concepts of the angle of strike (the strike) and the angle of dip (dip) are important. The strike and dip determine the position of the deposit in the earth’s interior (orientation relative to countries of the world or coordinate axes and slope relative to the horizontal plane). The elements of occurrence are very simple to find for regular bed deposits. When direct measurements are impossible, mining geometry offers procedures for indirect determinations. When the beds of rock and of the mineral are deformed into folds and parts of the beds are broken off and displaced, mining geometry works out methods to determine the elements of the folded shapes and methods of searching for the displaced parts of the beds. In this the methods of descriptive geometry are used extensively, in particular projections with numerical markings. Major credit for the development of these questions belongs to the Russian scientists P. M. Leontovskii and V. I. Bauman. As for displacements, mining geometry is used primarily to develop their classification and to find methods of searching for the displaced parts’ during mining work.
The development of mining production and of the mining and geological sciences places more complex tasks before mining geometry, and a great deal has been done by Soviet mining geometricians in solving them. To the extent that any bed represents a geometric body, the distribution of the mineral’s properties within this body also represents the shape of arrangement of elements of these properties in space. Ascertaining and drawing the sum total of these shapes and properties is the task of one of the subdivisions of mining geometry, called geometrization of the deposit. One of the founders of this subdivision is the Soviet scientist P. K. Sobolevskii. Questions of mining geometry abroad are presented in the most systematized form in the works of W. L. Donn and J. A. Shimer (United States, 1958).
REFERENCESSobolevskii, P. K. “Sovremennaia gornaia geometriia.” Sotsialisticheskaia rekonstruktsiia i nauka,1932, no. 7.
Ushakov, I. N. Gornaia geometriia,3rd ed. Moscow, 1962.
Ryzhov, P. A. Geometriia nedr,3rd ed. Moscow, 1964.