Cartesian coordinates represent points in a three-dimensional space using x, y, and z values, while polar coordinates describe points in a two-dimensional space using a radius (r) and an angle (θ). The conversion between these systems involves formulas where x = r cos(θ) and y = r sin(θ), with r calculated as the distance from the origin and θ as the angle from the positive x-axis. The discussion also touches on the distinction between two-dimensional polar coordinates and their three-dimensional counterparts, cylindrical and spherical coordinates. Clarifications on the terms nEW, nEN, and xERe relate to different types of numbers, such as rational and real. Understanding these concepts is essential for grasping the differences between coordinate systems.
