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Sphere Problem: Finding Latitude Radius

Sphere Problem: Finding Latitude Radius
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2016-10-27 09:52
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to solve for the latitude radius of a sphere using geometric construction methods. Key mathematical concepts include the geometric properties of a sphere and angle measurement. Using GeoGebra commands such as Point, CurveCartesian, and Sphere, the construction process is visually illustrated. Suitable for high school mathematics education, particularly in solid and coordinate geometry.

GeoGebra Commands & Parameters

  1. Point(zAxis) → B
  2. CurveCartesian(0, 0, (z(B) * t), t, -1, 1) → e
  3. Point(e) → J
  4. Sphere(A, B) → a
  5. CurveCartesian((z(B) * cos(t)), (z(B) * sin(t)), 0, t, 0, (2 * π)) → b
  6. CurveCartesian((r * cos(t)), (r * sin(t)), k, t, 0, (2 * π)) → d
  7. Point(d) → D
  8. Segment(C, D) → f
  9. Segment(A, D) → g
  10. Plane(A, B, D) → h
  11. Segment(A, E) → j
  12. Segment(C, A) → l
  13. Angle(E, A, D) → α
  14. AngularBisector(E, A, D) → m
  15. Point(m) → K
  16. PointIn(c) → L
  17. If(n > 0, "north") → text6
  18. If(n < 0, "south") → text7
  19. CornerThreeD(-1, 11) → M
  20. Plane(B, I, M) → o
  21. OrthogonalLine(N, o) → p
  22. CornerThreeD(-1, 1) → O
  23. CornerThreeD(-1, 7) → P
  24. IntersectPath(c, o) → f_1
  25. Min(abs(z(O)), z(P)) → v
  26. Segment(I, B) → g_1
  27. Circle(J, 3.5, g_1) → c_1
  28. Intersect(o, c_1) → Q, R
  29. IntersectPath(c, w) → h_1
  30. Segment((x(O), y(O), k), (x(O), y(P), k)) → q
  31. Segment((x(P), y(O), k), (x(P), y(P), k)) → s
  32. Segment((x(O), y(P), k), (x(P), y(P), k)) → t
  33. Segment((x(O), y(O), k), (x(P), y(O), k)) → i_1
  34. Plane(B, I, U) → u
  35. Intersect(h_1, u) → V

AI Drawing Prompt Reference

Draw a sphere with center A, and draw the equatorial plane passing through point B. Then, draw a circle on this plane with center J and radius 3.5. Next, draw a plane passing through points B and I, which intersects the equatorial plane to form a line that intersects the circle at points Q and R. Finally, draw another plane passing through points B, I, and M, which intersects the previous plane to form a line that intersects the sphere at point V.
The prompt above was compiled from the original drawing commands and is for reference only.