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Spherical Coordinates Demonstration

Spherical Coordinates Demonstration
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2022-07-20 13:39
TrigonometryCoordinate GeometrySolid Geometry
This example demonstrates the representation of points in spherical coordinates and their relationship with Cartesian coordinates. It involves core mathematical concepts such as spherical coordinates, polar coordinate transformation, and 3D spatial geometry. The construction uses GeoGebra commands like If, Segment, Angle, and Surface to create spheres, angles, and 3D surfaces. Suitable for high school and above students to learn about spatial geometry and coordinate transformations.

GeoGebra Commands & Parameters

  1. If(θ < 0, CurveCartesian[(abs((1 / 20 * t) + r / 4); (-t)), t, 0, (-θ)], CurveCartesian[((1 / 20 * t) + r / 4; t), t, 0, θ]) → a
  2. Segment((0, 0), (x(A), y(A))) → f
  3. Segment(A, (x(A), y(A))) → g
  4. Segment((x(A), 0, 0), (x(A), y(A), 0)) → Sxd
  5. Segment((0, y(A), 0), (x(A), y(A), 0)) → Syd
  6. Segment((x(A), 0, z(A)), (x(A), y(A), z(A))) → Sxu
  7. Segment((0, y(A), z(A)), (x(A), y(A), z(A))) → Syu
  8. Segment((0, 0, z(A)), (x(A), 0, z(A))) → Sxu1
  9. Segment((0, 0, z(A)), (0, y(A), z(A))) → Syu1
  10. Segment((x(A), 0, 0), (x(A), 0, z(A))) → Sxu2
  11. Segment((0, y(A), 0), (0, y(A), z(A))) → Syu2
  12. Segment((0, 0, 0), A) → SphR
  13. Angle((0, 0, 100), (0, 0, 0), A) → angR
  14. Angle((0, 0, 100), (0, 0, 0), A) → α
  15. Angle((0, 0, 100), (0, 0, 0), A) → β
  16. Surface(((r * cos(u)) * sin(v)), ((r * sin(u)) * sin(v)), (r * cos(v)), u, 0, (2 * pi), v, 0, pi) → s

AI Drawing Prompt Reference

Draw a 3D graph showing the relationship between spherical and Cartesian coordinates. Include a sphere, a point, an angle, and some 3D surfaces. The construction order should be: first draw the sphere, then add the point, then draw the angle, and finally create the 3D surfaces. Ensure the graph clearly shows the coordinate transformation relationship.
The prompt above was compiled from the original drawing commands and is for reference only.