(untitled) (Proceedings of Faculty of Civil Engineering, 2022)
In this paper, the properties of the logarithmic spiral given in the polar system are studied in more detail, thus the brief explanation of the polar system in the introduction. The paper deals with the property of a logarithmic spiral, which intersects all its radial rays at the same constant angle. Also, the natural equation of the logarithmic spiral is explained, and its equation is derived. The relationship between the curvature and the radius of the circle of curvature at each point of the logarithmic spiral is emphasized to define and derive the parametric equations of the evolved logarithmic spiral. It was proved that the logarithmic spiral and its evolute have the same natural equation.