Rotation Pattern

Rotation Pattern
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2017-11-03 22:28
This example demonstrates the creation of complex patterns through rotation and geometric constructions. It involves core mathematical concepts like rotation, polygon construction, function graphs, and solid geometry. Key GeoGebra commands and objects used include Polygon, Midpoint, Semicircle, and Sequence. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  2. Midpoint(E, A) → F
  3. Midpoint(A, B) → G
  4. Midpoint(B, C) → H
  5. Midpoint(C, D) → I
  6. Midpoint(D, E) → J
  7. Semicircle(J, I) → c
  8. Semicircle(I, H) → d
  9. Semicircle(H, G) → e
  10. Semicircle(G, F) → k
  11. Semicircle(F, J) → p
  12. Semicircle(J, F) → q
  13. Semicircle(F, G) → r
  14. Semicircle(G, H) → s
  15. Semicircle(H, I) → t
  16. Semicircle(I, J) → c_1
  17. Polygon(A, B, 3) → poly2, l, m, n, K
  18. Polygon(B, C, 3) → poly3, a, b, f_1, L
  19. Polygon(C, D, 3) → poly4, g_1, h_1, i_1, M
  20. Polygon(D, E, 3) → poly5, j_1, k_1, l_1, N
  21. Polygon(E, A, 3) → poly6, m_1, n_1, p_1, O
  22. Polygon(M, N, 5) → poly7, q_1, r_1, s_1, t_1, a_1, P, Q, R
  23. Semicircle(F, A) → d_1
  24. Semicircle(B, H) → e_1
  25. Semicircle(H, C) → c_2
  26. Semicircle(C, I) → d_2
  27. Semicircle(I, D) → e_2
  28. Semicircle(D, J) → f_2
  29. Semicircle(J, E) → g_2
  30. Semicircle(E, F) → h_2
  31. Semicircle(A, G) → k_2
  32. Semicircle(G, B) → p_2
  33. Sequence(Rotate[c, ((i * 2) * π / w), S], i, 1, w) → L_1
  34. Sequence(Rotate[c_1, ((i * 2) * π / w), S], i, 1, w) → L_2
  35. Sequence(Rotate[c_2, ((i * 2) * π / w), S], i, 1, w) → L_3
  36. Sequence(Rotate[d_2, ((i * 2) * π / w), S], i, 1, w) → L_4
  37. Sequence(Rotate[d_1, ((i * 2) * π / w), S], i, 1, w) → L_5
  38. Sequence(Rotate[d, ((i * 2) * π / w), S], i, 1, w) → L_6
  39. Sequence(Rotate[e, ((i * 2) * π / w), S], i, 1, w) → L_7
  40. Sequence(Rotate[e_1, ((i * 2) * π / w), S], i, 1, w) → L_8
  41. Sequence(Rotate[e_2, ((i * 2) * π / w), S], i, 1, w) → L_9
  42. Sequence(Rotate[f_2, ((i * 2) * π / w), S], i, 1, w) → L_{10}
  43. Sequence(Rotate[g_2, ((i * 2) * π / w), S], i, 1, w) → L_{11}
  44. Sequence(Rotate[h_2, ((i * 2) * π / w), S], i, 1, w) → L_{12}
  45. Sequence(Rotate[k_2, ((i * 2) * π / w), S], i, 1, w) → L_{13}
  46. Sequence(Rotate[p_2, ((i * 2) * π / w), S], i, 1, w) → L_{14}
  47. Sequence(Rotate[p, ((i * 2) * π / w), S], i, 1, w) → L_{15}
  48. Sequence(Rotate[k, ((i * 2) * π / w), S], i, 1, w) → L_{16}
  49. Sequence(Rotate[q, ((i * 2) * π / w), S], i, 1, w) → L_{17}
  50. Sequence(Rotate[r, ((i * 2) * π / w), S], i, 1, w) → L_{18}
  51. Sequence(Rotate[s, ((i * 2) * π / w), S], i, 1, w) → L_{19}
  52. Sequence(Rotate[t, ((i * 2) * π / w), S], i, 1, w) → L_{20}
  53. Sequence(Rotate[poly7, ((i * 2) * π / w), S], i, 1, w) → L_{21}

AI Drawing Prompt Reference

Draw a regular pentagon with five points A, B, C, D, and E. Then, find the midpoints of each pair of points and connect them to form a new regular pentagon. Next, draw semicircles with each midpoint as the center and the distance from the midpoint to the original pentagon vertex as the radius. Finally, rotate these semicircles around each midpoint to create a complex rotation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.