Spherical Coordinates: Interactive 3D Visualization of Coordinate Transformation

① This GeoGebra example dynamically illustrates a point P in 3D space using spherical coordinates, clearly showing the relationship between Cartesian (x,y,z) and spherical (ρ,φ,θ) representations. ② Core mathematical concepts include the spherical coordinate system, radial distance ρ, polar angle φ (angle from z-axis), azimuthal angle θ (projection in xy-plane), and the coordinate transformation formulas. ③ Construction details: uses Segment command to draw coordinate axes and auxiliary lines, Angle command to mark angles; objects include point P, its projection P', auxiliary lines L, Lperp, Lpara, and variables ρ, φ, θ, α, β, which can be adjusted via sliders or input to update the point's position in real time. ④ Suitable for upper high school or early university students learning multivariable calculus, vector analysis, or physics problems with spherical symmetry; also valuable for teachers demonstrating 3D coordinate transformations in class to enhance spatial reasoning.