周长演示：圆、正方形与任意三角形的周长对比

GeoGebra 命令及参数

1. Segment(A, B) → a
2. OrthogonalLine(A, a) → b
3. Distance(A, B) → Pmt
4. Circle(A, Pmt / 2) → d_1
5. Intersect(d_1, b, 2) → L
6. Rotate(L, 89°, A) → L'
7. CircleSector(A, L, L') → e_1
8. PointIn(e_1) → T1
9. Distance(A, T1) → ltriangle2
10. Circle(A, ltriangle2) → p_1
11. Intersect(p_1, a, 1) → N
12. Angle(N, A, T1) → RT1
13. Ellipse(A, T1, triangleparam / 2) → f_1
14. Point(f_1) → T2
15. If(alphatrianglestart ≟ (Angle[B, A, T2] * 360 / 2 / π), 1, 2) → casetriangle
16. If(go < alphatrianglestart / sumtriangle, 1, If[go < (alphatrianglestart + 180 - angleT2) / sumtriangle, 2, 3]) → phasetriangle1
17. If(casetriangle ≟ 2 ∧ phasetriangle1 ≟ 1, RT1 - ((go / alphatrianglestart * sumtriangle) * RT1)) → alpha2triangle1
18. Distance(T2, A) → ltriangle1
19. Circle(A, ltriangle1) → k_1
20. Intersect(k_1, a, 1) → M
21. Angle(M, A, T2) → RT2
22. If(casetriangle ≟ 1 ∧ phasetriangle1 ≟ 1, RT2 - ((go / alphatrianglestart * sumtriangle) * RT2)) → alpha1triangle1
23. Circle(A, lsquare) → g
24. Intersect(g, b, 2) → J
25. Rotate(J, 89°, A) → J'
26. CircleArc(A, J, J') → c_1
27. Point(c_1) → K
28. Angle(J, A, K) → alphasquarestart
29. If(go < alphasquarestart / sum, 1, If[go < (alphasquarestart + 90°) / sum, 2, If[go < (alphasquarestart + 180°) / sum, 3, 4]]) → phasesquare
30. Intersect(g, a, 1) → H
31. Circle(H, lsquare) → c
32. If(phasesquare ≟ 1, 90° + (alphasquarestart * (1 - (go * sum / alphasquarestart)))) → alphasquare1
33. Intersect(c, a, 1) → I
34. Line(D, b) → e
35. Distance(A, D) → parc
36. Circle(A, rcircle) → ccircle
37. Intersect(ccircle, b, 2) → C
38. Line(C, a) → f
39. Intersect(e, f) → E
40. Rotate(D, alphacircle, E) → D'
41. Angle(D, E, D') → α
42. CircleArc(E, D, D') → gcircle
43. Segment(A, D) → hcircle
44. Rotate(H, alphasquare1, A) → G
45. Rotate(G, -90°, A) → G'
46. Rotate(A, 90°, G) → F'
47. Segment(F', G') → i
48. Segment(F', G) → j
49. Segment(G, A) → d
50. Segment(A, G') → h
51. If(phasesquare ≟ 2, 90° + ((90 * (1 - ((go - alphasquarestart / sum) * sum / (90°)))))°) → alphasquare2
52. Rotate(I, alphasquare2, H) → I'
53. Angle(I, H, I') → β
54. Rotate(H, 90°, I') → H'
55. Angle(H, I', H') → γ
56. Rotate(I', 90°, H') → I''
57. Angle(I', H', I'') → δ
58. Segment(I', H') → k
59. Segment(H', I'') → l
60. Segment(I'', H) → m
61. Segment(H, A) → n
62. Circle(I, lsquare) → p
63. Intersect(p, a, 2) → F
64. If(phasesquare ≟ 3, ((90 * (1 - ((go - (alphasquarestart + 90°) / sum) * sum / (90°)))))°) → alphasquare3
65. Rotate(F, alphasquare3, I) → F'_1
66. Angle(F, I, F'_1) → ε
67. Rotate(I, -90°, F'_1) → I'_1
68. Angle(I'_1, F'_1, I) → ζ
69. Segment(I'_1, F'_1) → q
70. Segment(F'_1, I) → r
71. If(phasesquare ≟ 4, ((90 * (1 - ((go - (alphasquarestart + 180°) / sum) * sum / (90°)))))°) → alphasquare4
72. Rotate(B, alphasquare4, F) → B'
73. Angle(B, F, B') → η
74. Segment(B', F) → s
75. Segment(H, I) → t
76. Segment(I, F) → a_1
77. Angle(J, A, J') → θ
78. Angle(L, A, L') → ι
79. Distance(T1, T2) → ltriangleA
80. Rotate(M, alpha1triangle1, A) → M'
81. Angle(M, A, M') → κ
82. Rotate(N, alpha2triangle1, A) → N'
83. Angle(N, A, N') → λ
84. If(go < alphatrianglestart / sumtriangle, 1, If[go < (alphatrianglestart + 180 - angleT1) / sumtriangle, 2, 3]) → phasetriangle2
85. Segment(M', A) → h_1
86. Circle(M', ltriangleA) → q_1
87. Ray(M', A) → i_1
88. Intersect(q_1, i_1, 1) → O
89. Rotate(O, (-(angleT2°)), M') → O'
90. Angle(O', M', O) → μ
91. Segment(O', M') → j_1
92. Segment(O', A) → l_1
93. Segment(N', A) → b_1
94. Circle(N', ltriangleA) → g_1
95. Ray(N', A) → m_1
96. Intersect(g_1, m_1, 1) → P
97. Rotate(P, (-(angleT1°)), N') → P'
98. Angle(P', N', P) → ν
99. Segment(N', P') → n_1
100. Segment(P', A) → r_1
101. Circle(M, ltriangleA) → s_1
102. Intersect(s_1, a, 1) → Q
103. If(casetriangle ≟ 1 ∧ phasetriangle1 ≟ 2, (((180 - angleT2) * (1 - ((go - alphatrianglestart / sumtriangle) / (180 - angleT2) * sumtriangle))))°) → alpha1triangle2
104. Rotate(Q, alpha1triangle2, M) → Q'
105. Angle(Q, M, Q') → ξ
106. Segment(Q', M) → t_1
107. Circle(Q', ltriangle2) → c_2
108. Ray(Q', M) → a_2
109. Intersect(c_2, a_2, 1) → R
110. Rotate(R, (-(angleT1°)), Q') → R'
111. Angle(R', Q', R) → ο
112. Segment(Q', R') → b_2
113. If(casetriangle ≟ 1 ∧ phasetriangle1 ≟ 3, (((180 - angleT1) * (1 - ((go - (alphatrianglestart + 180 - angleT2) / sumtriangle) / (180 - angleT1) * sumtriangle))))°) → alpha1triangle3
114. Rotate(B, alpha1triangle3, Q) → B'_1
115. Angle(B, Q, B'_1) → ρ
116. Segment(B'_1, Q) → e_2
117. If(casetriangle ≟ 2 ∧ phasetriangle2 ≟ 2, (((180 - angleT1) * (1 - ((go - alphatrianglestart / sumtriangle) / (180 - angleT1) * sumtriangle))))°) → alpha2triangle2
118. Circle(N, ltriangleA) → d_2
119. Intersect(d_2, a, 2) → S
120. Rotate(S, alpha2triangle2, N) → S'
121. Angle(S, N, S') → σ
122. Circle(S', ltriangle1) → f_2
123. Ray(S', N) → g_2
124. Intersect(f_2, g_2, 1) → T
125. Rotate(T, (-(angleT2°)), S') → T'
126. Angle(T', S', T) → τ
127. Segment(S', T') → h_2
128. Segment(N, S') → i_2
129. Circle(S, ltriangle1) → k_2
130. If(casetriangle ≟ 2 ∧ phasetriangle2 ≟ 3, (((180 - angleT2) * (1 - ((go - (alphatrianglestart + 180 - angleT1) / sumtriangle) / (180 - angleT2) * sumtriangle))))°) → alpha2triangle3
131. Rotate(B, alpha2triangle3, S) → B'_2
132. Angle(B, S, B'_2) → υ
133. Segment(B'_2, S) → j_2
134. Segment(A, M) → l_2
135. Segment(M, Q) → m_2
136. Segment(A, N) → n_2
137. Segment(N, S) → p_2