Polar Coordinates in Engineering: Methods for Determining the Length of Curved Geometric Shapes

Abstract

This article is dedicated to an in-depth study of the practical significance of the polar coordinate system for determining the lengths of curved geometric shapes. Within the context of technical disciplines and engineering education, the article thoroughly describes the mechanisms of converting from polar to Cartesian coordinates, as well as differential and integral formulas used for calculating curve length. Specific examples are provided for calculating the lengths of typical geometric figures such as circles, cardioids, and ellipses, demonstrating the application of this theoretical knowledge in solving real engineering problems. This approach is widely used in the design of mechanical structures, automotive engineering, and aerospace systems. The article emphasizes that this work, connecting mathematical analysis and practical technical knowledge, holds significant value for students not only from an academic but also from a professional development perspective.