Spherical Coordinates by Noah
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This example demonstrates the construction of spherical coordinates, a three-dimensional coordinate system that describes points in space using radius, polar angle, and azimuthal angle. It utilizes Surface and Vector commands in GeoGebra. Suitable for high school and above students to learn about three-dimensional geometry and coordinate transformations.
GeoGebra Commands & Parameters
Surface(((p * sin(s)) * cos(t)), ((p * sin(s)) * sin(t)), (p * cos(s)), s, 0, π, t, 0, (2 * π)) → aVector((((p * sin(u)) * cos(v)), ((p * sin(u)) * sin(v)), (p * cos(u)))) → w
AI Drawing Prompt Reference
Draw a 3D surface in spherical coordinates with radius p, polar angle s, and azimuthal angle t. First, create a spherical surface with radius ranging from 0 to π and azimuthal angle from 0 to 2π. Then, draw a vector starting from the origin, pointing in the direction defined by radius p, polar angle u, and azimuthal angle v.
The prompt above was compiled from the original drawing commands and is for reference only.