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Deriving Sphere's Standard Form

Deriving Sphere's Standard Form
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2015-11-17 05:25
Coordinate GeometrySolid GeometryGeometric Construction
This example provides a 3D visual aid for students to understand how to derive the standard form of a sphere. It involves core math concepts like sphere, 3D space, and coordinate geometry. Key GeoGebra commands used include Intersect, Sphere, PointIn, Segment, OrthogonalLine, Point, and Polygon. Suitable for high school and above students learning about sphere equations.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → O
  2. Sphere(O, 1) → a
  3. PointIn(a) → A
  4. Segment(A, O) → X
  5. PointIn(a) → P
  6. Segment(O, P) → b
  7. OrthogonalLine(P, xOyPlane) → c
  8. Intersect(c, xAxis) → B_1
  9. Intersect(c, xAxis) → D
  10. Point(c) → B
  11. Polygon(O, P, B) → poly1, R_1, c_1, a_1
  12. Polygon(O, A, B) → poly2, f_1, Y_1, s
  13. Segment(B, A) → Y
  14. Segment(P, O) → R
  15. Segment(P, B) → Z