Cylindrical Coordinates: 3D Points and Geometric Transformations

①This GeoGebra example dynamically illustrates the position of points in cylindrical coordinates (r, θ, z) and their geometric transformations in 3D space, clearly showing the relationship between cylindrical and Cartesian coordinates. ②Core mathematical concepts include the definition of cylindrical coordinate systems, polar representation of radius r and angle θ, and the application of linear functions and geometric transformations (such as reflection and multiplication/scaling) in three dimensions. ③Construction highlights: using the Segment command to draw coordinate axes or radial distances, the Angle command to mark angle θ, and objects like zee, θ, r, O, C, g, D, a, E, f, h, α to build an interactive model, where α likely controls rotation or reflection. ④Suitable for high school to early university students, this resource aids in understanding 3D coordinate systems, spatial transformations, and parametric representations, serving as a visual teaching tool for mathematics.