Sfäärkoordinaatti

Sfäärkoordinaatti is a term that can refer to spherical coordinates in mathematics and physics. Spherical coordinates are a system of three coordinates that uniquely determine a point in three-dimensional space. Typically, these coordinates are represented by the radial distance from the origin, the polar angle (or zenith angle), and the azimuthal angle. The radial distance, often denoted by 'r', measures the straight-line distance from the origin to the point. The polar angle, often denoted by 'θ' (theta), measures the angle from the positive z-axis. The azimuthal angle, often denoted by 'φ' (phi), measures the angle in the xy-plane from the positive x-axis. This system is particularly useful in problems involving spheres or rotational symmetry. For example, in physics, it is commonly used to describe the position of particles in atomic orbitals or the motion of celestial bodies. The conversion between spherical coordinates and Cartesian coordinates (x, y, z) is well-defined. The radial coordinate is related to the Cartesian coordinates by r = sqrt(x^2 + y^2 + z^2). The polar angle is related by cos(θ) = z/r, and the azimuthal angle is related by tan(φ) = y/x. Different conventions exist for the order and ranges of these angles, so it is important to clarify the specific convention being used in any given context.