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G_9.04 Pyramids and cones_1

G_9.04 Pyramids and cones_1
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2022-09-07 22:15
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates constructing pyramids and cones using GeoGebra. Key mathematical concepts include solid geometry, coordinate geometry, and geometric transformations. Construction involves commands like Point, Intersect, Line, Cone, and tools such as OrthogonalLine and Midpoint. Suitable for high school students or college freshmen learning solid geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(zAxis) → B
  2. Intersect(yAxis, zAxis) → A
  3. Point(zAxis) → C
  4. Line(A, C) → f
  5. Cone(N, B, 1) → b_4, b_2, b_3
  6. Cylinder(A, B, 1) → a_2, c, d, e
  7. Cylinder(A, H, 1) → g, h, k, i
  8. Plane(D, xOyPlane) → p
  9. IntersectPath(p, b_4) → q
  10. Segment(D, B) → j
  11. Cone(q, (-j)) → n, n_2, n_3
  12. Plane(E, xOyPlane) → r
  13. IntersectPath(r, b_4) → s
  14. Segment(E, D) → m
  15. Cone(s, w) → a_1, c_1, b_1
  16. Cylinder(H, J, 1) → u, u_2, u_3, u_4
  17. Plane(F, xOyPlane) → p_1
  18. IntersectPath(p_1, b_4) → d_1
  19. Segment(F, B) → f_1
  20. Cone(d_1, (-f_1)) → j_1, j_2, j_3
  21. Cylinder(J, G, 1) → t, e_1, g_1, h_1
  22. Point(b_2) → I
  23. OrthogonalLine(I, xOyPlane) → k_1
  24. Point(k_1) → K
  25. Midpoint(I, K) → L
  26. Segment(I, L) → l_1
  27. Segment(L, K) → m_1
  28. Line(K, A) → q_1
  29. OrthogonalLine(A, q) → r_1
  30. OrthogonalLine(I, r_1, space) → s_1
  31. Intersect(s_1, r_1) → M
  32. Segment(I, M) → t_1
  33. Point(l_1) → O
  34. Line(O, t_1) → f_2
  35. OrthogonalLine(N, f_2, space) → g_2
  36. Intersect(g_2, f_2) → P
  37. Intersect(g_2, f_2) → Q
  38. Intersect(f_2, g_2) → R
  39. Segment(O, P) → h_2

AI Drawing Prompt Reference

In a 3D coordinate space, choose a vertical axis and another axis perpendicular to it, and set a vertex at their intersection. Mark two points on the vertical axis to form a second vertical reference line, connect the vertex to a point on that line to define a key direction line, then construct multiple cone and cylinder surfaces of radius 1 using these directions. Introduce several planes parallel to the horizontal reference plane, intersect each plane with the previously created cone surfaces to obtain spatial intersection curves, and from those curves generate additional cones using corresponding opposite directions for symmetry. Add visible edges by drawing segments determined by intersections between the cylinders and the cones, and use these to highlight the main silhouette and cross-sections.
The prompt above was compiled from the original drawing commands and is for reference only.