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Dynamic Demo of Regular Decagon and Pentadecagon

Dynamic Demo of Regular Decagon and Pentadecagon
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2017-05-15 08:54
PolygonAngleGeometric Construction
This example dynamically illustrates the geometric relationships and properties of a regular decagon and a regular pentadecagon. It involves core math concepts like polygons, angles, and geometric transformations. The construction uses commands such as Polygon, Segment, Circle, Center, Dilate, Rotate, and Angle in GeoGebra. Suitable for high school mathematics teaching or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 10) → poly1, f, p, C, D, E, F, G, H, I, J, g, h, i, j, k, l, m, n
  2. Polygon(E, D, 15) → poly2, q, f_1, g_1, h_1, i_1, j_1, k_1, K, L, M, N, r, O, P, Q, R, S, T, U, V, W, s, t, a, b, c, d, e
  3. Segment(D, E) → p_1
  4. Segment(E, F) → q_1
  5. Segment(D, K) → c_1
  6. Segment(K, L) → d_1
  7. Segment(L, M) → e_1
  8. Segment(M, N) → f_2
  9. Segment(N, O) → g_2
  10. Segment(O, P) → h_2
  11. Segment(P, Q) → i_2
  12. Segment(Q, R) → j_2
  13. Segment(R, S) → k_2
  14. Segment(S, T) → l_2
  15. Segment(T, U) → m_2
  16. Segment(U, V) → n_2
  17. Segment(V, W) → p_2
  18. Segment(W, E) → q_2
  19. Circle(A, B, C) → c_2
  20. Center(c_2) → Z
  21. Circle(L, M, N) → d_2
  22. Center(d_2) → A_1
  23. Dilate(Z, If[0 < o ≤ 1, 1 - o, 0], H) → Z'
  24. Segment(Z, Z') → l_1
  25. Rotate(poly1, If[1.5 < o ≤ 2.5, (((o - 1.5) * 36) * π / 180), (36 * π / 180)], Z) → poly1'
  26. Rotate(H, If[1.5 < o ≤ 2.5, (((o - 1.5) * 36) * π / 180), (36 * π / 180)], Z) → H'
  27. Segment(Z, H') → m_1
  28. Dilate(A_1, If[2.5 < o ≤ 3.5, 3.5 - o, 0], D) → B_1
  29. Segment(A_1, B_1) → n_1
  30. Rotate(poly2, If[3.5 < o ≤ 4.5, (((o - 3.5) * 24) * π / 180), (24 * π / 180)], A_1) → poly2'
  31. Rotate(A_1, If[3.5 < o ≤ 4.5, (((o - 3.5) * 24) * π / 180), (24 * π / 180)], A_1) → C_1
  32. Rotate(B_1, If[3.5 < o ≤ 4.5, (((o - 3.5) * 24) * π / 180), (24 * π / 180)], A_1) → D_1
  33. Segment(C_1, D_1) → r_1
  34. Polygon(F, E, W) → poly3, w, f_3, e_2
  35. Dilate(E, If[5 < o ≤ 6, 6 - o, 0], W) → E'
  36. Segment(E, E') → s_1
  37. Rotate(E, If[6 < o ≤ 7, ((o - 6) * π / 3), π / 3], E) → E'_1
  38. Rotate(E', If[6 < o ≤ 7, ((o - 6) * π / 3), π / 3], E) → E''
  39. Segment(E'_1, E'') → t_1
  40. Rotate(E, If[7 < o ≤ 8, (((o - 7) * 5) * π / 3), (5 * π / 3)], W) → E'_2
  41. Rotate(E', If[7 < o ≤ 8, (((o - 7) * 5) * π / 3), (5 * π / 3)], W) → E''_1
  42. Segment(E'_2, E''_1) → a_1
  43. Angle(A_1, K, Z) → α
  44. Rotate(C_1, If[8 < o ≤ 9, (((o - 8) * 108) * π / 180), (108 * π / 180)], K) → E_1
  45. Rotate(D_1, If[8 < o ≤ 9, (((o - 8) * 108) * π / 180), (108 * π / 180)], K) → F_1
  46. Segment(E_1, F_1) → b_1

AI Drawing Prompt Reference

Draw a dynamic illustration showing the geometric relationships and properties of a regular decagon and a regular pentadecagon. Start by constructing two polygons and connecting their sides to form segments. Create a circle centered at the center of the decagon and perform scaling and rotation operations based on this center. Apply similar operations to the pentadecagon, including scaling, rotation, and connecting sides. Finally, display the angle relationships between the two polygons and use dynamic parameters to control the rotation and scaling, making the图形 dynamically change.
The prompt above was compiled from the original drawing commands and is for reference only.