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Symmetry and Rotation Folding

Symmetry and Rotation Folding
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2020-01-18 02:06
MatrixTransformationGeometric Construction
This example demonstrates the folding process of symmetry and rotation. Key mathematical concepts include symmetry, rotation, and transformation. Using GeoGebra commands such as Polygon, Mirror, and Rotate, complex geometric shapes can be constructed. Suitable for middle school students and teachers to understand the basic principles of geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon((0, -4), (4, -4), (4, 0), (0, 0)) → poly1, a, b, c, d
  2. Mirror((0, 0), b) → H
  3. Mirror((4, 0), b) → G
  4. Mirror((4, -4), b) → F
  5. Mirror((0, -4), b) → E
  6. Polygon(E, F, G, H) → poly2, e, f, g, h
  7. Mirror(M, f) → M'_1
  8. Mirror(M'_1, g) → M''
  9. Mirror(P4, f) → P4'_3
  10. Mirror(P4'_3, g) → P4''
  11. Mirror(P3, f) → P3'_2
  12. Mirror(P3'_2, g) → P3''
  13. Mirror(P1, f) → P1'_1
  14. Mirror(P1'_1, g) → P1''
  15. Mirror(P2, f) → P2'_2
  16. Mirror(P2'_2, g) → P2''
  17. Mirror(N, f) → N'_1
  18. Mirror(N'_1, g) → N''
  19. Mirror(M, c) → M'
  20. Mirror(N, c) → N'
  21. Polygon(P1, P2, P3, P4, M, N) → polyhex1, i, l, m, n, p, q
  22. Rotate(P4, (((-plein) * 180))°, (4, y(P4))) → P4'_1
  23. Rotate((0, 0), (((-plein) * 180))°, (4, 0)) → A
  24. Rotate((0, -4), (((-plein) * 180))°, (4, -4)) → B
  25. Intersect(b, c) → C
  26. Intersect(b, a) → D
  27. Polygon(D, B, A, C) → poly1', d_1, b_1, a_1, c_1
  28. Mirror(P2, b) → P2'_1
  29. Mirror(P3, b) → P3'_1
  30. Mirror(P4, b) → P4'_2
  31. Intersect(a, d) → I
  32. Rotate(P1, (((plein - 1) * 180))°, (x(P1), 0)) → P11
  33. Rotate(P2, (((plein - 1) * 180))°, (x(P2), 0)) → P21
  34. Rotate(P4, (((plein - 1) * 180))°, (x(P4), 0)) → P41
  35. Rotate(P2'_1, (((plein - 1) * 180))°, (x(P2'_1), 0)) → P22
  36. Rotate(P4'_2, (((plein - 1) * 180))°, (x(P4'_2), 0)) → P42
  37. Rotate((0, -4), (((plein - 1) * 180))°, (0, 0)) → J
  38. Rotate((4, -4), (((plein - 1) * 180))°, (4, 0)) → J2
  39. Rotate((8, -4), (((plein - 1) * 180))°, (8, 0)) → J3
  40. Intersect(c, d) → K
  41. Polygon(K, J, J2, G) → poly3, k, j, j2, g_1
  42. Polygon(P1'_1, P2'_2, P3'_2, P4'_3, M'_1, N'_1) → polyhex4, r, s, t, e_1, f_1, i_1
  43. Polygon(J3, H, G, J2) → poly4, j3, h_1, g_2, j2_1
  44. Polygon(P1'', P2'', P3'', P4'', M'', N'') → polyhex3, j_1, k_1, l_1, m_1, n_1, p_1
  45. Mirror(P1, c) → P1'
  46. Mirror(P2, c) → P2'
  47. Mirror(P3, c) → P3'
  48. Mirror(P4, c) → P4'
  49. Polygon(P1', P2', P3', P4', M', N') → polyhex2, q_1, r_1, s_1, t_1, a_2, b_2
  50. Segment(M, P4) → c_2
  51. Midpoint(c_2) → O
  52. Midpoint(P4, O) → P
  53. Circle(S, T) → d_2
  54. Circle(U, V) → e_2
  55. Circle(W, Z) → f_2
  56. Ellipse(A_1, B_1, C_1) → h_2