Interactive Rectangle Transformation

GeoGebra Commands & Parameters

1. Segment(A, B) → a
2. Slope(a) → c
3. OrthogonalLine(A, a) → e
4. Point(e) → C
5. Ray(A, C) → d
6. Point(d) → D
7. Segment(A, D) → f
8. Line(D, a) → g
9. Line(B, f) → h
10. Intersect(g, h) → E
11. Segment(D, E) → i
12. Segment(E, B) → j
13. Midpoint(A, E) → F
14. Circle(A, (0.2 * Min[f, i])) → k
15. Intersect(k, f) → G,
16. Intersect(k, a, 1) → H
17. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
18. Vector(A, A') → u
19. CircleSector(A, H, G) → p
20. Translate(p, u) → p'
21. Rotate(p', If[1 < l ≤ 2, ((l - 1) * π / 2), 1.5707963267948966], B) → p''
22. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], E) → B'
23. Vector(B, B') → v
24. Translate(p'', v) → p'''
25. Rotate(p''', If[3 < l ≤ 4, ((l - 3) * π / 2), 1.5707963267948966], E) → q
26. Dilate(E, If[4 < l ≤ 5, 5 - l, 0], D) → E'
27. Vector(E, E') → w
28. Translate(q, w) → q'
29. Rotate(q', If[5 < l ≤ 6, ((l - 5) * π / 2), 1.5707963267948966], D) → q''
30. Dilate(D, If[6 < l ≤ 7, 7 - l, 0], F) → D'
31. Vector(D, D') → m
32. Segment(D, D') → n
33. Dilate(F, If[7 < l ≤ 8, 8 - l, 0], B) → F'
34. Segment(F, F') → r
35. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], F) → A'_1
36. Segment(A, A'_1) → s
37. Dilate(F, If[9 < l ≤ 10, 10 - l, 0], E) → F'_1
38. Segment(F, F'_1) → t
39. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
40. Angle(E, F, D) → α
41. Angle(B, A, F) → γ
42. Angle(F, A, D) → δ
43. Rotate(F, If[10 < l ≤ 11, ((l - 10) * α), α], F) → F'_2
44. Rotate(F'_1, If[10 < l ≤ 11, ((l - 10) * α), α], F) → I
45. Segment(F'_2, I) → t'
46. Rotate(F'_2, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → J
47. Rotate(I, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → I'
48. Segment(J, I') → t''
49. Rotate(J, If[12 < l ≤ 13, ((l - 12) * α), α], F) → J'
50. Rotate(I', If[12 < l ≤ 13, ((l - 12) * α), α], F) → I''
51. Segment(J', I'') → t'''
52. Segment(A, F) → c_1
53. Intersect(k, c_1) → K,
54. CircleSector(A, H, K) → f_1
55. CircleSector(A, K, G) → g_1
56. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], E) → A'_2
57. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], B) → A'_3
58. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], D) → A'_4
59. Vector(A, A'_3) → u_1
60. Vector(A, A'_2) → v_1
61. Vector(A, A'_4) → w_1
62. Translate(f_1, u_1) → h_1
63. Translate(f_1, v_1) → k_1
64. Translate(f_1, w_1) → p_1
65. Rotate(h_1, If[17 < l ≤ 18, ((l - 17) * (π / 2 + δ)), π / 2 + δ], B) → q_1
66. Rotate(p_1, If[17 < l ≤ 18, ((l - 17) * ((3 * π / 2) + δ)), (3 * π / 2) + δ], D) → r_1
67. Rotate(k_1, If[17 < l ≤ 18, ((l - 17) * π), 3.141592653589793], E) → s_1
68. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], E) → A'_5
69. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], D) → A'_6
70. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], B) → A'_7
71. Vector(A, A'_7) → i_1
72. Vector(A, A'_5) → j_1
73. Vector(A, A'_6) → l_1
74. Translate(g_1, l_1) → t_1
75. Translate(g_1, j_1) → c_2
76. Translate(g_1, i_1) → d_2
77. Rotate(d_2, If[19 < l ≤ 20, ((l - 19) * δ), δ], B) → e_2
78. Rotate(c_2, If[19 < l ≤ 20, ((-(l - 19)) * π), -3.141592653589793], E) → f_2
79. Rotate(t_1, If[19 < l ≤ 20, ((l - 19) * (π + δ)), π + δ], D) → g_2