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Double Cone Sphere Construction

Double Cone Sphere Construction
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2019-02-04 03:19
Solid GeometryTransformationGeometric Construction
This example demonstrates how to construct a spherical surface by combining two cones. It involves core mathematical concepts such as cones, spheres, symmetry, rotation, translation, etc. The construction uses GeoGebra commands and objects like Circle, Rotate, Polygon, Midpoint, CurveCartesian, Mirror, and Surface. Suitable for high school and above students to learn complex solid geometry constructions.

GeoGebra Commands & Parameters

  1. Circle((0, 0, 0), r, yAxis) → c_1
  2. Rotate(A, 30°, yAxis) → B
  3. Rotate(A, (-(30°)), yAxis) → C
  4. Polygon(C, B, 6, yAxis) → polígono1, f_1, G, g_1, h, i, k, l, D, E, F
  5. Midpoint(F, E) → H
  6. CurveCartesian((r / 2 * cos(t)), (r / 2 * sin(t)), z(H), t, 0, π) → a
  7. CurveCartesian((r * cos(t)), (r * sin(t)), 0, t, 0, π) → b
  8. Mirror(a, Plane[z = 0]) → c
  9. Rotate(Mirror[LC, Plane[y = 0]], α, yAxis) → l1
  10. Surface((a(t) * k) + ((1 - k) * b(t)), k, 0, 1, t, 0, π) → d
  11. Surface((b(t) * k) + ((1 - k) * c(t)), k, 0, 1, t, 0, π) → e
  12. Midpoint(B, C) → I
  13. Surface((I * k) + ((1 - k) * c(t)), k, 0, 1, t, 0, π) → g
  14. Surface((H * k) + ((1 - k) * a(t)), k, 0, 1, t, 0, π) → f
  15. Rotate(Mirror[LS, Plane[y = 0]], α, yAxis) → l2