Arc Length Formula S=Rθ

GeoGebra Commands & Parameters

1. Rotate((r, 0), 4, (0, 0)) → D
2. Rotate(D, If[11.5 < a ≤ 12.5, a - 11.5, 1], M) → D'
3. Line(M, D') → g_2
4. OrthogonalLine(D', g_2) → h_2
5. CircleArc(M, D, D') → c_2
6. Circle(D', r - c_2) → d_2
7. Intersect(d_2, h_2) → J_1, K_1
8. If(x(J_1) > x(K_1), J_1, K_1) → L_1
9. Segment((0, 0), (r, 0)) → f
10. Rotate((r, 0), 1, (0, 0)) → A
11. Rotate((r, 0), 2, (0, 0)) → B
12. Rotate((r, 0), 3, (0, 0)) → C
13. Rotate((r, 0), 5, (0, 0)) → E
14. Rotate((r, 0), -1, (0, 0)) → F
15. Rotate(f, If[0 < a ≤ 1, ((-a) * pi / 2), ((-pi)) / 2], (r, 0)) → f'
16. Rotate(G, If[1.5 < a ≤ 2.5, a - 1.5, 1], (0, 0)) → G'
17. CircleArc((0, 0), G, G') → c
18. Circle(G', r - c) → d
19. Line((0, 0), G') → g
20. OrthogonalLine(G', g) → h
21. Intersect(d, h, 2) → H
22. Segment(G', H) → i
23. Dilate(G, If[3 < a ≤ 4, 4 - a, 0], A) → G'_{1}
24. Vector(G, G'_{1}) → u
25. Translate(f, u) → f'_{1}
26. Line((0, 0), A) → j
27. OrthogonalLine(A, j) → k
28. Point(p) → I
29. Point(k) → J
30. Angle(J, A, I) → α
31. Rotate(f'_{1}, If[3 < a ≤ 4, ((-(a - 3)) * α), (-α)], G'_{1}) → l
32. Rotate(A, If[4 < a ≤ 5, a - 4, 1], (0, 0)) → A'
33. CircleArc((0, 0), A, A') → e
34. Circle(A', r - e) → q
35. Line((0, 0), A') → m
36. OrthogonalLine(A', m) → n
37. Intersect(q, n, 2) → K
38. Segment(A', K) → s
39. Dilate((0, 0), If[5.5 < a ≤ 6.5, 6.5 - a, 0], B) → L
40. Vector(M, L) → v
41. Translate(f, v) → f'_{2}
42. Line(M, B) → b
43. OrthogonalLine(B, b) → f_1
44. Point(t) → N
45. Point(f_1) → O
46. Angle(O, B, N) → β
47. Rotate(f'_{2}, If[5.5 < a ≤ 6.5, ((-(a - 5.5)) * β), (-β)], L) → g_1
48. Rotate(B, If[6.5 < a ≤ 7.5, a - 6.5, 1], (0, 0)) → B'
49. CircleArc(M, B, B') → c_1
50. Line(M, B') → h_1
51. OrthogonalLine(B', h_1) → i_1
52. Circle(B', r - c_1) → d_1
53. Intersect(d_1, i_1, 2) → P
54. Dilate(M, If[8 < a ≤ 9, 9 - a, 0], C) → M'
55. Vector(M, M') → w
56. Translate(f, w) → f'_{3}
57. Line(M, C) → k_1
58. OrthogonalLine(C, k_1) → l_1
59. Point(p_1) → Q
60. Point(l_1) → R
61. Angle(R, C, Q) → γ
62. Rotate(f'_{3}, If[8 < a ≤ 9, ((-(a - 8)) * γ), (-γ)], M') → m_1
63. Rotate(C, If[9 < a ≤ 10, a - 9, 1], M) → C'
64. CircleArc(M, C, C') → e_1
65. Line(M, C') → n_1
66. OrthogonalLine(C', n_1) → q_1
67. Circle(C', r - e_1) → r_1
68. Intersect(r_1, q_1) → S, B_1
69. Intersect(d_1, i_1, 1) → T
70. Dilate(M, If[10.5 < a ≤ 11.5, 11.5 - a, 0], D) → M'_{1}
71. Vector(M, M'_{1}) → u_1
72. Translate(f, u_1) → f'_{4}
73. Line(M, D) → a_1
74. OrthogonalLine(D, a_1) → b_1
75. Point(b_1) → U
76. Point(t_1) → V
77. Angle(U, D, V) → δ
78. Rotate(f'_{4}, If[10.5 < a ≤ 11.5, ((-(a - 10.5)) * δ), (-δ)], M'_{1}) → f_2
79. Intersect(d_2, h_2, 1) → W
80. Rotate(M, If[13 < a ≤ 14, ((a - 13) * pi / 2), pi / 2], G) → M'_{2}
81. Segment(G, M'_{2}) → j_2
82. If(x(P) ≤ x(T), P, T) → A_1
83. Segment(B', A_1) → j_1
84. If(y(B_1) < y(S), B_1, S) → C_1
85. Segment(C', C_1) → s_1
86. Rotate(G, If[14 < a ≤ 15, (-(a - 14)), -1], M) → G'_{2}
87. CircleArc(M, G'_{2}, G) → e_2
88. Line(M, G'_{2}) → k_2
89. Circle(G'_{2}, r - e_2) → p_2
90. OrthogonalLine(G'_{2}, k_2) → l_2
91. Intersect(p_2, l_2) → D_1, E_1
92. If(y(D_1) ≤ y(E_1), D_1, E_1) → F_1
93. Segment(G'_{2}, F_1) → m_2
94. Rotate(D, 1, M) → D'_{1}
95. Rotate(G, 0.5) → G'_{3}
96. Rotate(G, 1.5) → G'_{4}
97. Rotate(G, 2.5) → G'_{5}
98. Rotate(G, 3.5) → G'_{6}
99. Rotate(G, 4.5) → G'_{7}
100. Rotate(G, -0.5) → G'_{8}
101. If(0 < a < 14, G, G'_{2}) → H_1
102. If(0 < a ≤ 4, G', D'_{1}, 4 ≤ a ≤ 6.5, A', 6.5 < a ≤ 9, B', 9 < a ≤ 11.5, C', 11.5 < a ≤ 14, D') → I_1
103. Segment(G_1, I_1) → n_2
104. Angle(H_1, G_1, I_1) → θ
105. Segment(G_1, H_1) → q_2
106. Segment(D', Z) → i_2
107. CircleArc(G_1, H_1, I_1) → r_2