弧度概念与几何作图

GeoGebra 命令及参数

1. Segment((0, 0), (r, 0)) → f
2. Rotate((r, 0), 1, (0, 0)) → A
3. Rotate((r, 0), 2, (0, 0)) → B
4. Rotate((r, 0), 3, (0, 0)) → C
5. Rotate((r, 0), 4, (0, 0)) → D
6. Rotate((r, 0), 5, (0, 0)) → E
7. Rotate((r, 0), -1, (0, 0)) → F
8. Rotate(f, If[0 < a ≤ 1, ((-a) * pi / 2), ((-pi)) / 2], (r, 0)) → f'
9. Rotate(G, If[1.5 < a ≤ 2.5, a - 1.5, 1], (0, 0)) → G'
10. CircleArc((0, 0), G, G') → c
11. Circle(G', r - c) → d
12. Line((0, 0), G') → g
13. OrthogonalLine(G', g) → h
14. Intersect(d, h, 2) → H
15. Segment(G', H) → i
16. Dilate(G, If[3 < a ≤ 4, 4 - a, 0], A) → G'_{1}
17. Vector(G, G'_{1}) → u
18. Translate(f, u) → f'_{1}
19. Line((0, 0), A) → j
20. OrthogonalLine(A, j) → k
21. Point(p) → I
22. Point(k) → J
23. Angle(J, A, I) → α
24. Rotate(f'_{1}, If[3 < a ≤ 4, ((-(a - 3)) * α), (-α)], G'_{1}) → l
25. Rotate(A, If[4 < a ≤ 5, a - 4, 1], (0, 0)) → A'
26. CircleArc((0, 0), A, A') → e
27. Circle(A', r - e) → q
28. Line((0, 0), A') → m
29. OrthogonalLine(A', m) → n
30. Intersect(q, n, 2) → K
31. Segment(A', K) → s
32. Dilate((0, 0), If[5.5 < a ≤ 6.5, 6.5 - a, 0], B) → L
33. Vector(M, L) → v
34. Translate(f, v) → f'_{2}
35. Line(M, B) → b
36. OrthogonalLine(B, b) → f_1
37. Point(t) → N
38. Point(f_1) → O
39. Angle(O, B, N) → β
40. Rotate(f'_{2}, If[5.5 < a ≤ 6.5, ((-(a - 5.5)) * β), (-β)], L) → g_1
41. Rotate(B, If[6.5 < a ≤ 7.5, a - 6.5, 1], (0, 0)) → B'
42. CircleArc(M, B, B') → c_1
43. Line(M, B') → h_1
44. OrthogonalLine(B', h_1) → i_1
45. Circle(B', r - c_1) → d_1
46. Intersect(d_1, i_1, 2) → P
47. Dilate(M, If[8 < a ≤ 9, 9 - a, 0], C) → M'
48. Vector(M, M') → w
49. Translate(f, w) → f'_{3}
50. Line(M, C) → k_1
51. OrthogonalLine(C, k_1) → l_1
52. Point(p_1) → Q
53. Point(l_1) → R
54. Angle(R, C, Q) → γ
55. Rotate(f'_{3}, If[8 < a ≤ 9, ((-(a - 8)) * γ), (-γ)], M') → m_1
56. Rotate(C, If[9 < a ≤ 10, a - 9, 1], M) → C'
57. CircleArc(M, C, C') → e_1
58. Line(M, C') → n_1
59. OrthogonalLine(C', n_1) → q_1
60. Circle(C', r - e_1) → r_1
61. Intersect(r_1, q_1) → S, B_1
62. Intersect(d_1, i_1, 1) → T
63. Dilate(M, If[10.5 < a ≤ 11.5, 11.5 - a, 0], D) → M'_{1}
64. Vector(M, M'_{1}) → u_1
65. Translate(f, u_1) → f'_{4}
66. Line(M, D) → a_1
67. OrthogonalLine(D, a_1) → b_1
68. Point(b_1) → U
69. Point(t_1) → V
70. Angle(U, D, V) → δ
71. Rotate(f'_{4}, If[10.5 < a ≤ 11.5, ((-(a - 10.5)) * δ), (-δ)], M'_{1}) → f_2
72. Rotate(D, If[11.5 < a ≤ 12.5, a - 11.5, 1], M) → D'
73. CircleArc(M, D, D') → c_2
74. Line(M, D') → g_2
75. OrthogonalLine(D', g_2) → h_2
76. Circle(D', r - c_2) → d_2
77. Intersect(d_2, h_2, 2) → W
78. Intersect(d_2, h_2, 2) → Z
79. Rotate(M, If[13 < a ≤ 14, ((a - 13) * pi / 2), pi / 2], G) → M'_{2}
80. Segment(G, M'_{2}) → j_2
81. If(x(P) ≤ x(T), P, T) → A_1
82. Segment(B', A_1) → j_1
83. If(y(B_1) < y(S), B_1, S) → C_1
84. Segment(C', C_1) → s_1
85. Rotate(G, If[14 < a ≤ 15, (-(a - 14)), -1], M) → G'_{2}
86. CircleArc(M, G'_{2}, G) → e_2
87. Line(M, G'_{2}) → k_2
88. Circle(G'_{2}, r - e_2) → p_2
89. OrthogonalLine(G'_{2}, k_2) → l_2
90. Intersect(p_2, l_2) → D_1, E_1
91. If(y(D_1) ≤ y(E_1), D_1, E_1) → F_1
92. Segment(G'_{2}, F_1) → m_2
93. Rotate(D, 1, M) → D'_{1}
94. Rotate(G, 0.5) → G'_{3}
95. Rotate(G, 1.5) → G'_{4}
96. Rotate(G, 2.5) → G'_{5}
97. Rotate(G, 3.5) → G'_{6}
98. Rotate(G, 4.5) → G'_{7}
99. Rotate(G, -0.5) → G'_{8}
100. If(0 < a < 15, G, F) → H_1
101. If(0 < a < 5, A, D'_{1}, 5 ≤ a < 7.5, B, 7.5 ≤ a < 10, C, 10 ≤ a < 12.5, D, 12.5 ≤ a < 15, D'_{1}) → I_1
102. Segment(G_1, I_1) → n_2
103. Angle(H_1, G_1, I_1) → θ
104. Segment(G_1, H_1) → q_2
105. If(a < 5, "ian", "ians") → text8
106. Segment(D', Z) → i_2