Square Action! Interactive Exploration of Square Properties

GeoGebra Commands & Parameters

1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
2. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B) → A'
3. Segment(A, A') → f
4. Rotate(A, If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B) → A'_1
5. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B) → A''
6. Segment(A'_1, A'') → f'
7. Segment(A, B) → g
8. Segment(B, C) → h
9. Segment(C, D) → i
10. Segment(D, A) → j
11. Circle(C, (0.15 * j)) → k
12. Circle(B, (0.15 * j)) → p
13. Circle(A, (0.15 * j)) → q
14. Circle(D, (0.15 * j)) → r
15. Segment(A, C) → l
16. Segment(D, B) → m
17. Intersect(l, m) → E
18. Intersect(r, j, 1) → F
19. Intersect(r, m, 1) → G
20. Intersect(r, i, 1) → H
21. Intersect(k, i, 1) → I
22. Intersect(k, l, 1) → J
23. Intersect(k, h, 1) → K
24. Intersect(p, h, 1) → L
25. Intersect(p, m, 1) → M
26. Intersect(p, g, 1) → N
27. Intersect(q, g, 1) → O
28. Intersect(q, l, 1) → P
29. Intersect(q, j, 1) → Q
30. Rotate(A'_1, If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → R
31. Rotate(A'', If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → A'''
32. Segment(R, A''') → f''
33. CircleSector(B, L, N) → s
34. Rotate(R, If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → R'
35. Rotate(A''', If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → S
36. Segment(R', S) → f'''
37. Dilate(B, If[4 < e ≤ 5, 5 - e, 0], C) → B'
38. Vector(B, B') → u
39. Translate(s, u) → s'
40. Rotate(s', If[5 < e ≤ 6, ((e - 5) * π / 2), 1.5707963267948966], C) → s''
41. Dilate(C, If[6 < e ≤ 7, 7 - e, 0], D) → C'
42. Vector(C, C') → v
43. Translate(s'', v) → s'''
44. Rotate(s''', If[7 < e ≤ 8, ((e - 7) * π / 2), 1.5707963267948966], D) → t
45. Dilate(D, If[8 < e ≤ 9, 9 - e, 0], A) → D'
46. Vector(D, D') → w
47. Translate(t, w) → t'
48. Rotate(t', If[9 < e ≤ 10, ((e - 9) * π / 2), 1.5707963267948966], A) → t''
49. Dilate(A, If[10 < e ≤ 11, 11 - e, 0], E) → A'_2
50. Segment(A, A'_2) → n
51. Dilate(E, If[11 < e ≤ 12, 12 - e, 0], C) → E'
52. Segment(E, E') → a_1
53. Dilate(D, If[12 < e ≤ 13, 13 - e, 0], E) → D'_1
54. Segment(D, D'_1) → b_1
55. Dilate(E, If[13 < e ≤ 14, 14 - e, 0], B) → E'_1
56. Segment(E, E'_1) → c_1
57. Rotate(t, If[12 < e ≤ 13, (((e - 12) * 3) * π / 4), 2.356194490192345], D) → t'_1
58. Dilate(D, If[17 < e ≤ 18, 18 - e, 0], E) → D'_2
59. Vector(D, D'_2) → u_1
60. Translate(t'_1, u_1) → d_1
61. Rotate(E, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5707963267948966], E) → E'_2
62. Rotate(E'_1, If[14 < e ≤ 15, ((e - 14) * π / 2), 1.5708], E) → T
63. Segment(E'_2, T) → e_1
64. Rotate(E'_2, If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5707963267948966], E) → U
65. Rotate(T, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5708], E) → T'
66. Segment(U, T') → f_1
67. Rotate(U, If[17 < e ≤ 18, ((e - 17) * π / 2), 1.5707963267948966], E) → U'
68. Rotate(T', If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5708], E) → T''
69. Segment(U', T'') → g_1
70. CircleSector(B, L, M) → h_1
71. Dilate(B, If[18 < e ≤ 19, 19 - e, 0], C) → B'_1
72. Dilate(B, If[18 < e ≤ 19, 19 - e, 0], A) → B'_2
73. Dilate(B, If[18 < e ≤ 19, 19 - e, 0], D) → B'_3
74. Vector(B, B'_1) → v_1
75. Vector(B, B'_3) → w_1
76. Vector(B, B'_2) → i_1
77. Translate(h_1, v_1) → k_1
78. Translate(h_1, i_1) → p_1
79. Translate(h_1, w_1) → q_1
80. Rotate(k_1, If[19 < e ≤ 20, ((e - 19) * π / 2), 1.5707963267948966], C) → r_1
81. Rotate(p_1, If[19 < e ≤ 20, (((e - 19) * 3) * π / 2), 4.71238898038469], A) → t_1
82. Rotate(h_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], B) → c_2
83. Rotate(r_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], C) → d_2
84. Rotate(q_1, If[19 < e ≤ 20, ((e - 19) * π), 3.141592653589793], D) → s_1
85. Rotate(s_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], D) → e_2
86. Rotate(t_1, If[20.5 < e ≤ 21.5, ((e - 20.5) * π / 4), 0.7853981633974483], A) → f_2