Spherical Coordinates Demo by matheagle
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This example demonstrates the representation and transformation of points in spherical coordinate systems. It involves core mathematical concepts such as spherical coordinates, 3D spatial geometry, and trigonometric relationships. Construction highlights include using the Surface command to plot a sphere, Segment and Angle commands for geometric relations, and the If command for conditional logic. Key objects used are ρ_0, r_1, ϕ_0, θ_0, r, b, P, a, c, ϕ, Q, d, A, B, e, f, g, h, θ, α, i, text1, text2, text3. Suitable for high school and above students learning spatial coordinate transformations and 3D geometric constructions.
GeoGebra Commands & Parameters
Surface(((r(th, fi) * sin(fi)) * cos(th)), ((r(th, fi) * sin(fi)) * sin(th)), (r(th, fi) * cos(fi)), th, 0, θ_0, fi, 0, ϕ_0) → bSegment(P, (0, 0, 0)) → aSegment((0, 0, 0), (0, 0, z(P))) → cAngle(P, (0, 0, 0), (0, 0, ρ_0)) → ϕSegment(Q, (0, 0, 0)) → dSegment(A, Q) → eSegment(B, Q) → fSegment(P, (0, 0, z(P))) → gSegment(P, Q) → hIf(θ_0 ≤ π, Angle[(ρ_0, 0, 0), (0, 0, 0), Q], Angle[(ρ_0, 0, 0), (0, 0, 0), ((-ρ_0), 0, 0)]) → θIf(θ_0 > π, Angle[((-ρ_0), 0, 0), (0, 0, 0), Q]) → αSegment((0, 0), (x(P), y(P))) → i