Pallokoordinaatistojärjestelmä

Pallokoordinaatti, often translated as spherical coordinates, is a coordinate system that uses three numbers to uniquely determine the position of a point in three-dimensional space. Instead of the familiar Cartesian x, y, and z axes, spherical coordinates utilize a radial distance, an azimuthal angle, and a polar angle. The radial distance, typically denoted by the Greek letter rho (ρ), represents the straight-line distance from the origin to the point. The azimuthal angle, often denoted by theta (θ), measures the angle from the positive x-axis in the xy-plane. Finally, the polar angle, usually denoted by phi (φ), measures the angle from the positive z-axis. The convention for the ranges of these angles can vary, but commonly, ρ is non-negative, θ is between 0 and 2π (or 0 and 360 degrees), and φ is between 0 and π (or 0 and 180 degrees). This system is particularly useful in fields involving spheres, rotations, or problems with spherical symmetry, such as physics, astronomy, and engineering. Converting between spherical and Cartesian coordinates is a common operation, with formulas relating (ρ, θ, φ) to (x, y, z) and vice versa. The geometric interpretation of these three values provides an intuitive way to describe locations on or within a sphere.