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Volume Transformation Demo

Volume Transformation Demo
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2014-01-24 01:25
Solid GeometryCalculusTransformationGeometric Construction
In collections Connolly Geometry Volume
This example dynamically constructs geometric solids using sliders to visually demonstrate volume transformation. It involves core math concepts like volume, similarity transformation, arithmetic mean, definite integral, and Pythagorean theorem. Construction uses commands like Polygon, Dilate, Ray, Translate, Vector, Circle, Segment, Line, Intersect, OrthogonalLine, Semicircle, PointIn, and objects A, B, C, D, poly1, etc. Suitable for high school mathematics teaching to introduce volume and similarity transformation applications.

GeoGebra Commands & Parameters

  1. Polygon(C, D, B) → poly1, b, c, d
  2. Dilate(C, a, A) → C'_1
  3. Dilate(D, a, A) → D'_1
  4. Dilate(B, a, A) → B'_1
  5. Polygon(C'_1, D'_1, B'_1) → poly1'_1, b', c', d'
  6. Ray(A, C) → e
  7. Ray(A, B) → f
  8. Ray(A, D) → g
  9. Translate(C, Vector[(horz, vert)]) → C'_2
  10. Translate(D, Vector[(horz, vert)]) → D'_2
  11. Translate(B, Vector[(horz, vert)]) → B'_2
  12. Polygon(C'_2, D'_2, B'_2) → poly1'_2, b'_1, c'_1, d'_1
  13. Vector(C, C'_2) → u
  14. Vector(B, B'_2) → v
  15. Vector(D, D'_2) → w
  16. Polygon(E, G, 5) → poly2, h, i, j, l, m, I, J, K
  17. Circle(L, M) → p_2
  18. Segment(N, O) → n
  19. Vector(N, O) → z
  20. Translate(p_2, z) → p'
  21. Line(M, L) → q
  22. Intersect(p_2, q, 2) → P
  23. OrthogonalLine(P, q) → r
  24. OrthogonalLine(M, q) → s
  25. OrthogonalLine(L, q) → a_1
  26. Intersect(p', r, 1) → Q
  27. Intersect(p', s, 1) → R
  28. Line(Q, R) → b_1
  29. Intersect(a_1, b_1) → S
  30. Segment(Q, P) → c_1
  31. Segment(R, M) → d_1
  32. Segment(Q, P) → e_1
  33. Segment(R, M) → f_1
  34. Polygon(Q, P, M, R) → poly3, q_1, p_1, m_1, r_1
  35. Semicircle(Q, R) → g_1
  36. Semicircle(M, P) → h_1
  37. Line(K, I) → p
  38. Line(G, E) → i_1
  39. Line(J, p) → j_1
  40. Vector(T, V) → u_1
  41. Translate(poly2, u_1) → poly2'
  42. PointIn(poly2') → U
  43. PointIn(poly2') → W
  44. PointIn(poly2') → Z
  45. PointIn(poly2') → A_1
  46. PointIn(poly2') → B_1
  47. Segment(B_1, K) → k_1
  48. Segment(U, E) → l_1
  49. Segment(W, G) → n_1
  50. Segment(Z, I) → s_1
  51. Segment(A_1, J) → t_1
  52. Segment(B_1, K) → a_2
  53. Segment(U, E) → b_2
  54. Segment(W, G) → c_2
  55. Segment(Z, I) → d_2
  56. Segment(U, W) → e_2
  57. Segment(W, Z) → f_2
  58. Segment(A_1, Z) → g_2
  59. Segment(A_1, B_1) → h_2
  60. Segment(B_1, U) → i_2
  61. Segment(K, J) → j_2
  62. Segment(J, I) → k_2
  63. Segment(I, G) → l_2
  64. Segment(E, G) → m_2
  65. Segment(K, E) → n_2
  66. Vector(C_1, D_1) → v_1
  67. Translate(C, v_1) → C'
  68. Translate(D, v_1) → D'
  69. Translate(B, v_1) → B'
  70. Polygon(C', D', B') → poly1', b'_2, c'_2, d'_2
  71. Segment(E_1, C') → q_2
  72. Segment(B', F_1) → r_2
  73. Segment(D', D) → s_2
  74. Segment(E_1, F_1) → a_3
  75. Segment(C', D') → c_3
  76. Segment(D', B') → d_3
  77. Segment(B', C') → e_3
  78. Segment(E_1, D) → t_2
  79. Segment(D, F_1) → b_3