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Spherical Coordinates Demo

Spherical Coordinates Demo
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2020-01-16 17:48
TrigonometryCoordinate GeometrySolid GeometryParametric EquationGeometric Construction
In collections 学习 GeoGebra 经典应用
This example demonstrates the conversion between spherical coordinates (r,θ,φ) and Cartesian coordinates (X,Y,Z), and the construction of a sphere in 3D space. Key mathematical concepts include coordinate transformations, solid geometry, and parametric equations. GeoGebra commands like Intersect, Sphere, and Segment are used, along with objects such as r,θ,φ,X,Y,Z. Suitable for high school and university students learning spatial geometry, coordinate systems, and parametric equations.

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 in 3D a sphere in space whose center is obtained from the intersection of the z-axis with the y-axis. Use that intersection point as the center and construct the sphere with radius r. Next, find the intersection point of the z-axis with the x-axis, and include a corresponding segment/connection from that point to the relevant point on the construction so the axes-to-sphere relationship is clearly visible. Emphasize the geometric links among the coordinate axes’ intersection points, the center, and the sphere determined by r.
The prompt above was compiled from the original drawing commands and is for reference only.