Dynamic Geometric Illustration

GeoGebra Commands & Parameters

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
3. Midpoint(A, E) → I
4. Midpoint(B, F) → J
5. Midpoint(C, G) → K
6. Midpoint(D, H) → L
7. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], D) → A'
8. Dilate(E, If[0 < a ≤ 1, 1 - a, 0], H) → E'
9. Segment(A, A') → n
10. Segment(E, E') → p
11. Rotate(A, If[1 < a ≤ 2, ((a - 1) * π / 2), π / 2], D) → A'_1
12. Rotate(A', If[1 < a ≤ 2, ((a - 1) * π / 2), π / 2], D) → A''
13. Segment(A'_1, A'') → n'
14. Rotate(E, If[1 < a ≤ 2, ((a - 1) * π / 2), π / 2], H) → E'_1
15. Rotate(E', If[1 < a ≤ 2, ((a - 1) * π / 2), π / 2], H) → E''
16. Segment(E'_1, E'') → p'
17. Rotate(A'_1, If[2 < a ≤ 3, ((a - 2) * π / 2), π / 2], C) → M
18. Rotate(A'', If[2 < a ≤ 3, ((a - 2) * π / 2), π / 2], C) → A'''
19. Segment(M, A''') → n''
20. Rotate(E'_1, If[2 < a ≤ 3, ((a - 2) * π / 2), π / 2], G) → N
21. Rotate(E'', If[2 < a ≤ 3, ((a - 2) * π / 2), π / 2], G) → E'''
22. Segment(N, E''') → p''
23. Rotate(M, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], B) → M'
24. Rotate(A''', If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], B) → O
25. Segment(M', O) → n'''
26. Rotate(N, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], F) → N'
27. Rotate(E''', If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], F) → P
28. Segment(N', P) → p'''
29. Angle(A, D, C) → α
30. Angle(D, C, B) → β
31. Angle(B, A, D) → γ
32. Angle(H, G, F) → δ
33. Angle(G, F, E) → ε
34. Angle(F, E, H) → ζ
35. Dilate(A, If[5 < a ≤ 6, 6 - a, 0], I) → A'_2
36. Segment(A, A'_2) → q
37. Dilate(I, If[6 < a ≤ 7, 7 - a, 0], E) → I'
38. Segment(I, I') → r
39. Rotate(A, If[7 < a ≤ 8, ((-(a - 7)) * π), (-π)], I) → A'_3
40. Rotate(A'_2, If[7 < a ≤ 8, ((-(a - 7)) * π), (-π)], I) → Q
41. Segment(A'_3, Q) → q'
42. Dilate(B, If[8 < a ≤ 9, 9 - a, 0], J) → B'
43. Segment(B, B') → s
44. Dilate(J, If[9 < a ≤ 10, 10 - a, 0], F) → J'
45. Segment(J, J') → t
46. Rotate(B, If[10 < a ≤ 11, ((-(a - 10)) * π), (-π)], J) → B'_1
47. Rotate(B', If[10 < a ≤ 11, ((-(a - 10)) * π), (-π)], J) → B''
48. Segment(B'_1, B'') → s'
49. Dilate(C, If[11 < a ≤ 12, 12 - a, 0], K) → C'
50. Segment(C, C') → b
51. Dilate(K, If[12 < a ≤ 13, 13 - a, 0], G) → K'
52. Segment(K, K') → c
53. Rotate(C, If[13 < a ≤ 14, ((a - 13) * π), π], K) → C'_1
54. Rotate(C', If[13 < a ≤ 14, ((a - 13) * π), π], K) → C''
55. Segment(C'_1, C'') → b'
56. Dilate(D, If[14 < a ≤ 15, 15 - a, 0], L) → D'
57. Segment(D, D') → d
58. Dilate(L, If[15 < a ≤ 16, 16 - a, 0], H) → L'
59. Segment(L, L') → e
60. Rotate(D, If[16 < a ≤ 17, ((a - 16) * π), π], L) → D'_1
61. Rotate(D', If[16 < a ≤ 17, ((a - 16) * π), π], L) → D''
62. Segment(D'_1, D'') → d'
63. Dilate(I, If[18 < a ≤ 19, 19 - a, 0], J) → I'_1
64. Segment(I, I'_1) → f_1
65. Rotate(I, If[19 < a ≤ 20, ((a - 19) * π / 2), π / 2], I) → I'_2
66. Rotate(I'_1, If[19 < a ≤ 20, ((a - 19) * π / 2), π / 2], I) → R
67. Segment(I'_2, R) → g_1
68. Rotate(I'_2, If[20 < a ≤ 21, ((a - 20) * π / 2), π / 2], L) → S
69. Rotate(R, If[20 < a ≤ 21, ((a - 20) * π / 2), π / 2], L) → R'
70. Segment(S, R') → h_1
71. Rotate(S, If[21 < a ≤ 22, ((a - 21) * π / 2), π / 2], K) → S'
72. Rotate(R', If[21 < a ≤ 22, ((a - 21) * π / 2), π / 2], K) → R''
73. Segment(S', R'') → i_1
74. Polygon(I, J, K, L) → q1, i_2, j_1, k_1, l_1
75. Min({Distance[A, B], Distance[I, J], Distance[E, F]}) → o
76. Circle(B, (0.25 * o)) → c_1
77. Segment(C, B) → m_1
78. Intersect(c_1, m_1) → T,
79. Rotate(T, If[22 < a ≤ 23, ((a - 22) * π / 2), π / 2], B) → T'
80. CircleSector(B, T, T') → d_1
81. Dilate(B, If[24 < a ≤ 25, 25 - a, 0], I) → B'_2
82. Vector(B, B'_2) → u
83. Translate(d_1, u) → e_1
84. Line(I, n'') → n_1
85. Circle(I, 5) → p_1
86. Intersect(p_1, n_1) → U, V
87. Angle(J, I, U) → η
88. Rotate(e_1, If[24 < a ≤ 25, ((a - 24) * ((2 * π) - η)), (2 * π) - η], B'_2) → q_1
89. Angle(E, H, G) → θ