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Symmetries of Regular Polygons - Rotational Symmetry

Symmetries of Regular Polygons - Rotational Symmetry
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2019-05-17 23:02
PolygonTrigonometryGeometric Construction
This example demonstrates the rotational symmetry of regular polygons. It involves core math concepts like rotation symmetry, angles, and geometric construction. Constructed using GeoGebra commands such as Polygon, Midpoint, Segment, and Intersect. Suitable for middle school and above mathematics education or self-learning to understand geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Polygon(D, E, 4) → poly2, d, e, f, g, F, G
  3. Polygon(H, I, 5) → poly3, h, i, j, k, l, J, K, L
  4. Polygon(M, N, 6) → poly4, m, R, n, p, q, r, s, O, P, Q
  5. Polygon(S, T, 8) → poly5, t, V, W, Z, A_1, B_1, a_1, b_1, c_1, d_1, e_1, f_1, g_1, U
  6. Polygon(C_1, D_1, 9) → poly6, h_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1
  7. Midpoint(A, C) → L_1
  8. Midpoint(B, A) → M_1
  9. Segment(L_1, B) → r_1
  10. Segment(C, M_1) → s_1
  11. Intersect(r_1, s_1) → N_1
  12. Midpoint(C, B) → O_1
  13. Segment(O_1, A) → t_1
  14. Segment(E, G) → a_2
  15. Segment(D, F) → b_2
  16. Intersect(a_2, b_2) → P_1
  17. Midpoint(I, H) → Q_1
  18. Midpoint(H, L) → R_1
  19. Midpoint(L, K) → S_1
  20. Segment(K, Q_1) → c_2
  21. Segment(I, S_1) → d_2
  22. Intersect(c_2, d_2) → T_1
  23. Segment(M, P) → e_2
  24. Segment(Q, N) → f_2
  25. Intersect(e_2, f_2) → U_1
  26. Segment(B_1, V) → g_2
  27. Segment(A_1, U) → h_2
  28. Intersect(g_2, h_2) → V_1
  29. Midpoint(H_1, G_1) → W_1
  30. Midpoint(G_1, F_1) → Z_1
  31. Segment(C_1, W_1) → i_2
  32. Segment(K_1, Z_1) → j_2
  33. Midpoint(I_1, H_1) → A_2
  34. Segment(D_1, A_2) → k_2
  35. Intersect(i_2, j_2) → B_2

AI Drawing Prompt Reference

Draw six regular polygons with 3, 4, 5, 6, 8, and 9 sides respectively, each placed separately. For each polygon, draw diagonals connecting non-adjacent vertices such that they intersect at a common interior point, which is the center of the polygon. Specifically, for each polygon, select two vertices that are separated by one vertex, connect them to form a diagonal, then select another pair of such vertices and connect them, ensuring the two diagonals intersect at the center. Clearly show all polygon edges, the diagonals, and the central intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.