At present, strengthening the practical orientation of education in the training of specialists is one of the mostrelevant scientific and practical challenges. This issue can be effectively addressed by systematically motivating theeducational process and integrating theoretical knowledge with practical application. The main objective of this study is toscientifically demonstrate the practical application of knowledge acquired in mathematics and automation of technologicalprocesses.The article provides a detailed analysis of solving geometric problems on computer numerical control (CNC) machinetools. Within the framework of the study, an interpolation algorithm ensuring the movement of machine working elementsis implemented, and the principles of its operation as well as methods for organizing motion along a specified trajectoryare examined. The scientific novelty of the research lies in substantiating the possibility of high-precision machining basedon accurate determination of cutting tool motion geometry and correct formulation of the geometric problem.The practical significance of the work is determined by the development of a real CNC machining control program usinginterpolation algorithms within the part coordinate system. The study employs general scientific and specialized researchmethods, including observation, comparison, analysis, and synthesis. The obtained results demonstrate that the proposedapproach enhances productivity, improves machining accuracy, and reduces time consumption.