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Growing Pyramid

Growing Pyramid
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2017-08-05 10:07
FunctionTrigonometrySolid Geometry
This example demonstrates the dynamic changes of a pyramid. It involves key mathematical concepts such as geometric transformations, trigonometric functions, and polynomial functions. Using GeoGebra commands like If, Point, Polygon, Segment, Rotate, and Midpoint, a dynamic pyramid model is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. If(A2 > 0, (A2, B2), 0) → C2
  2. If(A3 > 0, (A3, B3), 0) → C3
  3. If(A4 > 0, (A4, B4), " ") → C4
  4. If(A5 > 0, (A5, B5), " ") → C5
  5. If(A6 > 0, (A6, B6), " ") → C6
  6. If(A7 > 0, (A7, B7), " ") → C7
  7. If(A8 > 0, (A8, B8), " ") → C8
  8. If(A9 > 0, (A9, B9), " ") → C9
  9. If(A10 > 0, (A10, B10), " ") → C10
  10. If(A11 > 0, (A11, B11), " ") → C11
  11. If(A12 > 0, (A12, B12), " ") → C12
  12. If(A13 > 0, (A13, B13), " ") → C13
  13. If(A14 > 0, (A14, B14), " ") → C14
  14. If(A15 > 0, (A15, B15), " ") → C15
  15. If(A16 > 0, (A16, B16), " ") → C16
  16. If(A17 > 0, (A17, B17), " ") → C17
  17. If(A18 > 0, (A18, B18), " ") → C18
  18. If(A19 > 0, (A19, B19), " ") → C19
  19. If(A20 > 0, (A20, B20), " ") → C20
  20. If(A21 > 0, (A21, B21), " ") → C21
  21. If(A22 > 0, (A22, B22), " ") → C22
  22. If(A23 > 0, (A23, B23), " ") → C23
  23. If(A24 > 0, (A24, B24), " ") → C24
  24. If(A25 > 0, (A25, B25), " ") → C25
  25. If(A26 > 0, (A26, B26), " ") → C26
  26. If(A27 > 0, (A27, B27), " ") → C27
  27. If(A28 > 0, (A28, B28), " ") → C28
  28. If(A29 > 0, (A29, B29), " ") → C29
  29. If(A30 > 0, (A30, B30), " ") → C30
  30. If(A31 > 0, (A31, B31), " ") → C31
  31. If(A32 > 0, (A32, B32), " ") → C32
  32. If(A33 > 0, (A33, B33), " ") → C33
  33. If(A34 > 0, (A34, B34), " ") → C34
  34. If(A35 > 0, (A35, B35), " ") → C35
  35. Point(Circle[A, 1]) → B
  36. Point(Circle[D, 1]) → E
  37. Polygon((5.094626308379802, 4.705492463825604), (7.094626308379808, 4.705492463825604), 3) → poly3
  38. Segment(D, E) → j
  39. Point(Circle[C, 2]) → F
  40. Rotate(F, 60°, C) → F'
  41. Midpoint(C, F') → G
  42. Midpoint(C, F) → H
  43. Midpoint(F, F') → I
  44. Point(Circle[Q, 4]) → R
  45. Segment(Q, R) → f
  46. Polygon(Q, R, 3) → poly1, g, h, i, S
  47. Midpoint(S, Q) → T
  48. Midpoint(S, R) → U
  49. Midpoint(R, Q) → V
  50. Polygon(Q, V, T) → poly2, t_5, q_5, v
  51. Polygon(V, U, R) → poly7, r_5, v_1, u
  52. Polygon(U, T, S) → poly23, s_5, u_1, t_6
  53. Tool1(O) → poly14, poly15, g_2, h_2, poly16, k, l, c, f_1, g_1, h_1, i_1
  54. Intersect(h_2, g_2) → P
  55. Intersect(h_1, g_1) → W
  56. Tool1(W) → poly17, poly18, p_3, q_3, poly19, i_2, i_3, j_3, k_3, l_3, m_3, n_3
  57. Tool1(P) → poly20, poly21, e_3, f_4, poly22, r_3, s_3, t_3, a_3, b_3, c_3, d_3

AI Drawing Prompt Reference

Draw a dynamic pyramid with a triangular base. Start by drawing a triangular base, then rotate to generate the pyramid's sides around the base's center point, and finally add lines connecting the apex to the base.
The prompt above was compiled from the original drawing commands and is for reference only.