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Dynamic and Modifiable Composite Solid

Dynamic and Modifiable Composite Solid
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2017-08-07 21:47
FunctionTrigonometrySolid GeometryGeometric Construction
This example demonstrates a dynamic and modifiable composite solid, showcasing the combination of different geometric shapes through parameter adjustments. Core mathematical concepts include solid geometry, similar triangles, piecewise functions, histograms, difference and slope, and trigonometry. The construction leverages GeoGebra commands and objects such as Ray, Point, Cylinder, Circle, CircleArc, Intersect, Vector, Translate, and Segment. Suitable for high school and above, it serves as a comprehensive teaching tool for solid geometry, functions, and geometric integrations.

GeoGebra Commands & Parameters

  1. Ray((0, 0, 0), (0, 0, 1)) → f
  2. Point(f) → B
  3. Cylinder(C, B, r) → a, d, e, b
  4. Circle(f, D) → g
  5. Circle(f, A) → k
  6. CircleArc(B, D, R) → q
  7. Intersect(f, q, 1) → S
  8. CircleArc(B, S, K) → s
  9. CircleArc(B, F, S) → p
  10. CircleArc(B, S, L) → t
  11. CircleArc(B, G, S) → c_1
  12. CircleArc(B, S, M) → d_1
  13. CircleArc(B, H, S) → e_1
  14. CircleArc(B, S, N) → f_1
  15. Intersect(f_1, p, 2) → Q
  16. CircleArc(B, I, Q) → g_1
  17. CircleArc(B, Q, O) → h_1
  18. Intersect(h_1, p, 2) → T
  19. CircleArc(B, J, T) → k_1
  20. CircleArc(B, T, P) → p_1
  21. Vector(D, A) → u
  22. Translate(F, u) → F'
  23. Translate(G, u) → G'
  24. Translate(H, u) → H'
  25. Translate(H, u) → H'_1
  26. Translate(I, u) → I'
  27. Translate(J, u) → J'
  28. Translate(K, u) → K'
  29. Translate(L, u) → L'
  30. Translate(M, u) → M'
  31. Translate(g, u) → g'
  32. Translate(O, u) → O'
  33. Translate(N, u) → N'
  34. Translate(P, u) → P'
  35. Translate(D, u) → D'
  36. Segment(G, G') → h
  37. Segment(H, H'_1) → m
  38. Segment(I, I') → n
  39. Segment(J, J') → i_1
  40. Segment(K, K') → j_1
  41. Segment(L, L') → l_1
  42. Segment(M, M') → m_1
  43. Segment(N, N') → n_1
  44. Segment(O, O') → q_1
  45. Segment(P, P') → r_1
  46. Segment(D, A) → s_1
  47. Segment(F, F') → t_1