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Gigantotron Similarity Demo

Gigantotron Similarity Demo
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2013-04-25 07:31
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
In collections Transformations
This example demonstrates the principles of geometric similarity, prism volume, and surface area calculations. Core math concepts include area, volume, equations, arithmetic operations, isosceles triangles, trapezoids, and geometric transformations. Construction involves commands like Line, OrthogonalLine, Rotate, Circle, Intersect, Polygon, Segment, and objects such as A, B, a, b, b', H, W, L, c, d, e, C, D, E, f, g, i, j, k, l, F, G, m, H_1, n, I, poly1, a_1, c_1, f_1, d_1, poly2, d_2, g_1, i_1, f_2, poly3, c_2, f_3, i_2. Suitable for high school students and teachers for solid geometry, similarity, and computational lessons.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Rotate(b, 30*°, A) → b'
  4. Circle(A, H) → c
  5. Circle(A, W) → d
  6. Circle(A, L) → e
  7. Intersect(c, a, 2) → C
  8. Intersect(d, b, 1) → D
  9. Intersect(e, b', 1) → E
  10. OrthogonalLine(C, a) → f
  11. OrthogonalLine(D, b) → g
  12. OrthogonalLine(E, a) → i
  13. Line(D, b') → j
  14. Line(E, a) → k
  15. Line(C, b') → l
  16. Intersect(f, g) → F
  17. Intersect(i, j) → G
  18. Line(G, a) → m
  19. Intersect(k, l) → H_1
  20. Line(F, b') → n
  21. Intersect(m, n) → I
  22. Polygon(A, C, F, D) → poly1, a_1, c_1, f_1, d_1
  23. Polygon(D, G, I, F) → poly2, d_2, g_1, i_1, f_2
  24. Polygon(C, F, I, H_1) → poly3, c_2, f_3, i_2, h_1
  25. Segment(G, E) → p
  26. Segment(H_1, E) → q
  27. Segment(E, A) → r
  28. Line(A, D) → h
  29. OrthogonalLine(G, h) → s
  30. Intersect(h, s) → J
  31. Circle(J, 2) → t
  32. Intersect(t, h, 2) → K
  33. Line(A, D) → b_1
  34. OrthogonalLine(K, b_1) → e_1
  35. Line(K, d_2) → j_1
  36. Circle(K, scale * H) → k_1
  37. Circle(K, scale * W) → p_1
  38. Circle(K, scale * L) → q_1
  39. Intersect(k_1, e_1, 2) → M
  40. Intersect(p_1, b_1, 2) → N
  41. Intersect(q_1, j_1, 2) → O
  42. Line(N, e_1) → l_1
  43. Line(M, b_1) → m_1
  44. Line(N, j_1) → n_1
  45. Line(O, e_1) → r_1
  46. Line(M, j_1) → s_1
  47. Intersect(l_1, m_1) → P
  48. Intersect(r_1, s_1) → Q
  49. Line(Q, b_1) → a_2
  50. Polygon(K, N, P, M) → poly4, k_2, n_2, p_2, m_2
  51. Segment(K, O) → b_2
  52. Segment(O, Q) → e_2
  53. Line(N, h_1) → t_1
  54. Line(O, k_2) → g_2
  55. Line(Q, g_2) → h_2
  56. Intersect(t_1, g_2) → R
  57. Line(R, n_2) → j_2
  58. Intersect(h_2, j_2) → S
  59. Polygon(N, R, S, P) → poly5, n_3, r_2, s_2, p_3
  60. Polygon(S, Q, M, P) → poly6, s_3, q_2, m_3, p_4
  61. Segment(O, R) → l_2

AI Drawing Prompt Reference

Draw a 3D geometric figure with three similar quadrilaterals. Start by drawing a line segment AB, then construct a line b perpendicular to AB, and rotate b to get b'. Draw three circles with radii H, W, and L centered at A, and find points C, D, and E by intersecting these circles with line a and b. Construct perpendicular lines f, g, and i from C, D, and E, and lines j, k, and l from D, E, and C, then find points F, G, and H_1 by intersecting these lines. Finally, construct quadrilaterals ACFD, DGIF, and CFIH_1.
The prompt above was compiled from the original drawing commands and is for reference only.