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Spherical Coordinates by GeoGebra Team

Spherical Coordinates by GeoGebra Team
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2019-05-23 16:23
FunctionTrigonometryCoordinate GeometrySolid GeometryParametric Equation
In collections Learn GeoGebra Classic
This example demonstrates the conversion between spherical coordinates (r, θ, φ) and Cartesian coordinates (X, Y, Z) in 3D space. Key mathematical concepts include spherical coordinates, triple angles, Cartesian coordinates, and 3D geometry. The construction uses GeoGebra commands like Intersect, Sphere, and Segment to visualize and manipulate points in both coordinate systems. Suitable for high school and above mathematics education to understand and apply spherical coordinates in 3D geometry.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, yAxis) → B
  2. Sphere(B, r) → a
  3. Intersect(zAxis, xAxis) → C
  4. Segment(C, A) → b

AI Drawing Prompt Reference

Draw a sphere centered at the origin in 3D space with three coordinate axes visible. Create a point at the intersection of the z-axis and y-axis, and draw a sphere centered at this point. Then, create a point at the intersection of the z-axis and x-axis, and connect this point to the origin to form a line segment. These elements illustrate the conversion between spherical and Cartesian coordinates, suitable for high school and above mathematics education.
The prompt above was compiled from the original drawing commands and is for reference only.