ALGORITHM FOR APPROXIMATE DIVISION OF AN ANGLE BY CONVERGENT SERIES. APPLICATIONS AND ACCURACY ASSESSMENT
https://doi.org/10.59982/18294359-25.2-zs-19
Abstract
This work proposes an algorithm for approximate calculation by convergent series, which allows solving many current problems. Such approaches are especially relevant in the modern world, where numerical modeling and approximate calculations play a central role in many areas of science and engineering. In case of construction problems of geometry, which also have applications in a number of important areas, certain difficulties arise in solving them. In particular, such a problem is the problem of dividing an angle into three equal parts using only a compass and a ruler. In a number of practical applications, approximate division with some accuracy is also sufficient. In this work, the algorithm for approximate calculation by convergent series is considered on the example of the problem of dividing an angle into three equal parts, for which the calculation code was compiled using the Python program. The algorithm under consideration can have practical applications in such areas as:
•Design and manufacture of gears.
•Control of movements of machines with numerical coordinates using Computer Numerical Control (CNC)
.•Design of extended optical components (special prisms, diffraction gratings or specialized lenses) in optical, scientific and other devices.
•Working with geometric data or performing spatial transformations in Machine Learning and neural networks, etc.
Keywords: Angle division, algorithm, numerical series, convergence, absolute error, calculation accuracy.
PAGES :183-190