MathPlotAI Logo MathPlotAI

Dynamic Regular Nonagon Demonstration

Dynamic Regular Nonagon Demonstration
Loading the math board and drawing, please wait…
2019-05-13 19:20
PolygonGeometric Construction
This example dynamically demonstrates the geometric construction and properties of a regular nonagon. It involves core mathematical concepts such as polygon construction, symmetry, rotations, and dilations. The construction uses commands like Polygon, Line, Segment, Circle, Intersect, Rotate, and Dilate in GeoGebra. Suitable for high school mathematics education to illustrate the symmetry and transformation properties of regular polygons.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 9) → poly1, f, C, D, E, F, G, H, I, g, h, i, j, k, l, m, n
  2. Line(F, D) → p
  3. Line(F, B) → q
  4. Line(D, B) → r
  5. Segment(F, E) → s
  6. Circle(F, E) → c
  7. Intersect(c, q, 2) → J
  8. Line(E, I) → t
  9. Segment(F, G) → a
  10. Segment(G, H) → b
  11. Segment(H, I) → d
  12. Segment(I, A) → e
  13. Segment(A, B) → f_1
  14. Segment(B, C) → g_1
  15. Segment(C, D) → h_1
  16. Segment(D, E) → i_1
  17. Rotate(B, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → B'
  18. Rotate(C, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → C'
  19. Segment(B', C') → j_1
  20. Rotate(C, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → C'_1
  21. Rotate(D, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → D'
  22. Segment(C'_1, D') → k_1
  23. Rotate(D, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → D'_1
  24. Rotate(E, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → E'
  25. Segment(D'_1, E') → l_1
  26. Rotate(F, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → F'
  27. Rotate(E, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → E'_1
  28. Segment(F', E'_1) → s'
  29. Rotate(F, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → F'_1
  30. Rotate(G, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → G'
  31. Segment(F'_1, G') → a'
  32. Rotate(G, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → G'_1
  33. Rotate(H, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → H'
  34. Segment(G'_1, H') → b'
  35. Rotate(H, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → H'_1
  36. Rotate(I, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → I'
  37. Segment(H'_1, I') → d'
  38. Rotate(I, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → I'_1
  39. Rotate(A, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → A'
  40. Segment(I'_1, A') → e'
  41. Rotate(A, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → A'_1
  42. Rotate(B, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → B'_1
  43. Segment(A'_1, B'_1) → n_1
  44. Rotate(poly1, If[1.5 < o ≤ 2.5, (((o - 1.5) * 2) * π / 9), (2 * π / 9)], Center[Circle[A, B, C]]) → poly1'
  45. Dilate(E'_1, If[3 < o ≤ 4, 4 - o, 0], J) → K
  46. Segment(E', K) → m_1
  47. Dilate(J, If[4 < o ≤ 5, 5 - o, 0], A'_1) → J'
  48. Segment(J, J') → p_1
  49. Dilate(C'_1, If[5 < o ≤ 6, 6 - o, 0], A'_1) → L
  50. Segment(C'_1, L) → q_1
  51. Rotate(D'_1, If[7 < o ≤ 8, ((-(o - 7)) * π / 3), ((-π)) / 3], E'_1) → M
  52. Rotate(E', If[7 < o ≤ 8, ((-(o - 7)) * π / 3), ((-π)) / 3], E'_1) → E''
  53. Segment(M, E'') → r_1
  54. Rotate(C'_1, If[8 < o ≤ 9, (((o - 8) * 2) * π / 9), (2 * π / 9)], A'_1) → N
  55. Rotate(L, If[8 < o ≤ 9, (((o - 8) * 2) * π / 9), (2 * π / 9)], A'_1) → L'
  56. Segment(N, L') → s_1

AI Drawing Prompt Reference

Draw a dynamic regular nonagon to demonstrate its geometric construction and symmetry. Start by creating a central nonagon and connecting its adjacent vertices with line segments. From one vertex, draw a circle centered at the midpoint of a side, intersecting adjacent sides to get new points. Rotate and scale these points dynamically to illustrate the symmetry and transformation properties of the nonagon.
The prompt above was compiled from the original drawing commands and is for reference only.