Dynamic Geometry Illustration by Tim Brzezinski (4)

GeoGebra Commands & Parameters

1. Circle(A, B) → c
2. Distance(A, B) → a
3. PointIn(b) → C_1
4. Semicircle(A, C_1) → d
5. Semicircle(C_1, A) → e
6. Intersect(c, d, 1) → D_1
7. Intersect(c, e, 1) → C
8. Line(C_1, C) → f
9. Line(C_1, D_1) → g
10. Line(C, g) → h
11. Intersect(c, h) → F, D
12. Line(C_1, D) → i
13. Intersect(c, i, 2) → E
14. Line(C, E) → j
15. Intersect(g, j) → G
16. Angle(A, D_1, G) → α
17. Angle(C_1, C, A) → β
18. Dilate(C_1, If[0 < k ≤ 1, 1 - k, 0], G) → H
19. Midpoint(C, C_1) → I
20. Dilate(C_1, If[0 < k ≤ 1, 1 - k, 0], I) → J
21. Segment(C_1, J) → l
22. Segment(C_1, H) → m
23. Dilate(G, If[0 < k ≤ 1, 1 - k, 0], G) → G'
24. Dilate(A, If[1 < k ≤ 2, 2 - k, 0], D_1) → A'
25. Dilate(A, If[1 < k ≤ 2, 2 - k, 0], C) → A'_1
26. Segment(A, A') → n
27. Segment(A, A'_1) → p
28. Dilate(G, If[1 < k ≤ 2, 2 - k, 0], D_1) → G'_1
29. Dilate(I, If[1 < k ≤ 2, 2 - k, 0], C) → I'
30. Segment(G, G'_1) → q
31. Segment(I, I') → r
32. Rotate(A, 90°, C) → A'_2
33. Angle(A, C, A'_2) → γ
34. Circle(C_1, (0.4 * Distance[C_1, G])) → t
35. Angle(G, C_1, C) → δ
36. Intersect(t, m) → L,
37. Rotate(L, If[4 < k ≤ 5, ((k - 4) * δ), δ], C_1) → L'
38. Dilate(C_1, If[5.5 < k ≤ 6.5, 6.5 - k, 0], C) → M
39. Vector(C_1, M) → u
40. Dilate(E, If[7 < k ≤ 8, 8 - k, 0], C_1) → E'
41. Segment(E, E') → h_1
42. Dilate(C, If[8.5 < k ≤ 9.5, 9.5 - k, 0], E) → C'_1
43. Dilate(E, If[9.5 < k ≤ 10.5, 10.5 - k, 0], G) → E'_1
44. Rotate(C_1, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → N
45. Rotate(G, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → G'_2
46. CircleArc(A, D_1, C) → e_1
47. Point(e_1) → O
48. Line(O, C_1) → n_1
49. Line(D_1, n_1) → p_1
50. Intersect(e_1, p_1) → P, Q
51. Line(O, Q) → f_1
52. Midpoint(O, Q) → K
53. Circle(O, (0.5 * Distance[O, K])) → s
54. Intersect(s, n_1) → R, S
55. Intersect(s, f_1, 1) → T
56. Angle(R, O, T) → ε
57. Line(C, Q) → g_1
58. Intersect(n_1, g_1) → U
59. Intersect(c, n_1) → V, W
60. Dilate(O, If[4 < k ≤ 5, 5 - k, 0], U) → O'
61. Segment(O, O') → q_1
62. Dilate(U, If[5 < k ≤ 6, 6 - k, 0], W) → U'
63. Segment(U, U') → r_1
64. Ray(O, R) → s_1
65. Dilate(W, If[6 < k ≤ 7, 7 - k, 0], C_1) → W'
66. Segment(W, W') → t_1
67. Circle(Q, 3) → c_1
68. Intersect(c_1, p_1, 1) → Z
69. Ray(Q, Z) → a_1
70. Dilate(D_1, If[7 < k ≤ 8, 8 - k, 0], Q) → A_1
71. Segment(D_1, A_1) → b_1
72. Rotate(R, If[8.5 < k ≤ 9.5, ((k - 8.5) * ε), ε], O) → R'
73. CircleSector(O, R, R') → d_1
74. Dilate(O, If[10 < k ≤ 11, 11 - k, 0], Q) → O'_1
75. Vector(O, O'_1) → v
76. Translate(d_1, v) → c_2
77. Dilate(C, If[11 < k ≤ 12, 12 - k, 0], U) → C'
78. Segment(C, C') → i_1
79. Dilate(U, If[12 < k ≤ 13, 13 - k, 0], Q) → U'_1
80. Segment(U, U'_1) → j_1
81. Angle(O, U, A) → ζ
82. Dilate(A, If[13.5 < k ≤ 14.5, 14.5 - k, 0], U) → A'_3
83. Segment(A, A'_3) → k_1
84. Dilate(O, If[13.5 < k ≤ 14.5, 14.5 - k, 0], U) → O'_2
85. Segment(O, O'_2) → l_1
86. Rotate(O, If[15 < k ≤ 16, ((k - 15) * π), π], U) → O'_3
87. Rotate(O'_2, If[15 < k ≤ 16, ((k - 15) * π), π], U) → B_1
88. Segment(O'_3, B_1) → m_1
89. Segment(O, O'_1) → f_2
90. Circle(O, 1) → d_2
91. Intersect(d_2, f_1, 1) → E_1
92. Ray(O, E_1) → g_2