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Rotational Symmetry of Special Shapes

Rotational Symmetry of Special Shapes
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2015-01-16 19:56
PolygonTransformation
This example demonstrates the rotational symmetry of special shapes, focusing on the concept of rotational symmetry. Using GeoGebra commands such as Point, Polygon, Centroid, and Rotate, specific polygons with particular rotational symmetry are constructed. Suitable for middle school and above students or teachers to understand the concept of rotational symmetry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → E
  4. Point(xAxis) → F
  5. Point(xAxis) → M
  6. Point(xAxis) → P
  7. Point(xAxis) → S
  8. Polygon(Z, A_1, 3) → poly1, a, b, c, B_1
  9. Polygon(A, B, C, D) → poly2, a_1, b_1, c_1, d
  10. Polygon(E, F, G, H) → poly3, e, f, g, h
  11. Polygon(I, J, K, L) → poly4, i, j, k, l
  12. Polygon(M, P, O, N) → poly5, m, p, o, n
  13. Polygon(Q, R, S, T) → poly6, q, r, s, t
  14. Polygon(U, V, W) → poly7, w, u, v
  15. Polygon(E_1, F_1, 5) → poly8, l_1, m_1, n_1, p_1, q_1, G_1, H_1, I_1
  16. Polygon(J_1, K_1, 6) → poly9, r_1, O_1, s_1, t_1, a_2, b_2, c_2, L_1, M_1, N_1
  17. Polygon(P_1, Q_1, 8) → poly10, d_2, S_1, T_1, U_1, V_1, W_1, e_2, f_2, g_2, h_2, i_2, j_2, k_2, R_1
  18. Centroid(poly9) → C_1
  19. Centroid(poly8) → D_1
  20. Centroid(poly10) → Z_1
  21. Centroid(poly1) → A_2
  22. Centroid(poly2) → B_2
  23. Centroid(poly3) → C_2
  24. Centroid(poly4) → D_2
  25. Centroid(poly5) → E_2
  26. Centroid(poly7) → F_2
  27. Rotate(A, angle, B_2) → A'
  28. Rotate(B, angle, B_2) → B'
  29. Rotate(C, angle, B_2) → C'
  30. Rotate(D, angle, B_2) → D'
  31. Polygon(A', B', C', D') → poly2', a', b', c', d'
  32. Rotate(E, angle, C_2) → E'
  33. Rotate(F, angle, C_2) → F'
  34. Rotate(G, angle, C_2) → G'
  35. Rotate(H, angle, C_2) → H'
  36. Polygon(E', F', G', H') → poly3', e', f', g', h'
  37. Rotate(I, angle, D_2) → I'
  38. Rotate(J, angle, D_2) → J'
  39. Rotate(K, angle, D_2) → K'
  40. Rotate(L, angle, D_2) → L'
  41. Polygon(I', J', K', L') → poly4', i', j', k', l'
  42. Rotate(M, angle, E_2) → M'
  43. Rotate(P, angle, E_2) → P'
  44. Rotate(O, angle, E_2) → O'
  45. Rotate(N, angle, E_2) → N'
  46. Polygon(M', P', O', N') → poly5', m', p', o', n'
  47. Rotate(U, angle, F_2) → U'
  48. Rotate(V, angle, F_2) → V'
  49. Rotate(W, angle, F_2) → W'
  50. Polygon(U', V', W') → poly7', w', u', v'
  51. Rotate(poly1, angle, A_2) → poly1'
  52. Rotate(poly8, angle, D_1) → poly8'
  53. Rotate(Q, angle, R) → Q'
  54. Rotate(R, angle, R) → R'
  55. Rotate(S, angle, R) → S'
  56. Rotate(T, angle, R) → T'
  57. Polygon(Q', R', S', T') → poly6', q', r', s', t'
  58. Rotate(poly9, angle, C_1) → poly9'
  59. Rotate(poly10, angle, Z_1) → poly10'

AI Drawing Prompt Reference

Draw a special polygon with rotational symmetry. Start by creating points A, B, E, F, M, P, S on the x-axis, then draw polygons poly1, poly2, poly3, poly4, poly5, and poly6. Next, draw polygons poly8, poly9, and poly10, and find their centroids C1, D1, Z1, A2, B2, C2, D2, E2, and F2. Finally, rotate polygons around points B2, C2, D2, E2, and F2 to generate new polygons poly2', poly3', poly4', poly5', and poly6'.
The prompt above was compiled from the original drawing commands and is for reference only.