几何作图驱动的最值与回归示例：锥体截面相关构型

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. OrthogonalLine(C, b) → f
3. Circle(C, 1) → d
4. Intersect(d, f, 1) → D
5. Segment(A, D) → g
6. OrthogonalLine(D, g) → h
7. Circle(D, 1) → e
8. Intersect(e, h, 2) → E
9. Segment(A, E) → i
10. OrthogonalLine(E, i) → j
11. Circle(E, 1) → k
12. Intersect(k, j, 2) → F
13. Segment(A, F) → l
14. OrthogonalLine(F, l) → m
15. Circle(F, 1) → p
16. Intersect(p, m, 2) → G
17. Segment(A, G) → n
18. OrthogonalLine(G, n) → q
19. Circle(G, 1) → r
20. Intersect(r, q, 2) → H
21. Segment(A, H) → s
22. OrthogonalLine(H, s) → t
23. Circle(H, 1) → c_1
24. Intersect(c_1, t, 2) → I
25. Segment(A, I) → f_1
26. OrthogonalLine(I, f_1) → g_1
27. Circle(I, 1) → d_1
28. Intersect(d_1, g_1, 2) → J
29. Segment(A, J) → h_1
30. OrthogonalLine(J, h_1) → i_1
31. Circle(J, 1) → e_1
32. Intersect(e_1, i_1, 2) → K
33. Segment(A, K) → j_1
34. OrthogonalLine(K, j_1) → k_1
35. Circle(K, 1) → p_1
36. Intersect(p_1, k_1, 2) → L
37. Segment(A, L) → l_1
38. OrthogonalLine(L, l_1) → m_1
39. Circle(L, 1) → q_1
40. Intersect(q_1, m_1, 2) → M
41. Segment(A, M) → n_1
42. OrthogonalLine(M, n_1) → r_1
43. Circle(M, 1) → s_1
44. Intersect(s_1, r_1, 2) → N
45. Segment(A, N) → t_1
46. OrthogonalLine(N, t_1) → a_1
47. Circle(N, 1) → c_2
48. Intersect(c_2, a_1, 2) → O
49. Segment(A, O) → b_1
50. OrthogonalLine(O, b_1) → f_2
51. Circle(O, 1) → d_2
52. Intersect(d_2, f_2, 2) → P
53. Segment(A, P) → g_2
54. OrthogonalLine(P, g_2) → h_2
55. Circle(P, 1) → e_2
56. Intersect(e_2, h_2, 2) → Q
57. Segment(A, Q) → i_2
58. OrthogonalLine(Q, i_2) → j_2
59. Circle(Q, 1) → k_2
60. Intersect(k_2, j_2, 2) → R
61. Segment(A, R) → l_2
62. Segment(C, D) → m_2
63. Segment(D, E) → n_2
64. Segment(E, F) → p_2
65. Segment(F, G) → q_2
66. Segment(G, H) → r_2
67. Segment(H, I) → s_2
68. Segment(I, J) → t_2
69. Segment(J, K) → a_2
70. Segment(K, L) → b_2
71. Segment(L, M) → f_3
72. Segment(M, N) → g_3
73. Segment(N, O) → h_3
74. Segment(O, P) → i_3
75. Segment(P, Q) → j_3
76. Segment(Q, R) → k_3
77. Angle(C, B, A) → α
78. Angle(D, C, A) → β
79. Angle(E, D, A) → γ
80. Angle(F, E, A) → δ
81. Angle(G, F, A) → ε
82. Angle(H, G, A) → ζ
83. Angle(I, H, A) → η
84. Angle(J, I, A) → θ
85. Angle(K, J, A) → ι
86. Angle(L, K, A) → κ
87. Angle(M, L, A) → λ
88. Angle(N, M, A) → μ
89. Angle(O, N, A) → ν
90. Angle(P, O, A) → ξ
91. Angle(Q, P, A) → ο
92. Angle(R, Q, A) → ρ
93. Segment(A, B) → l_3
94. Segment(C, B) → m_3
95. Segment(C, A) → n_3
96. RotateText(text1_{1}, atand(Slope[n_3])) → text2
97. RotateText(text3, atand(Slope[g])) → text4
98. Midpoint(f_1) → S
99. Midpoint(n_1) → T
100. RotateText(text5, pi / 4) → text6
101. RotateText(text7, atan(Slope[g])) → text8
102. RotateText(text9, atand(Slope[i])) → text10
103. Rotate(D, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → D'
104. Rotate(E, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → E'
105. Segment(D', E') → p_3
106. Rotate(D', If[1 < o ≤ 2, ((-(o - 1)) * pi), (-pi)], D') → D''
107. Rotate(E', If[1 < o ≤ 2, ((o - 1) * pi), pi], D') → E''
108. Segment(D'', E'') → q_3
109. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], I) → A'
110. Vector(A, A') → u
111. Translate(C, u) → C'
112. Translate(A, u) → A'_{1}
113. Segment(C', A'_{1}) → r_3
114. Translate(C, u) → C'_{1}
115. Angle(A, I, C'_{1}) → σ
116. Rotate(C', If[4 < o ≤ 5, ((-(o - 4)) * σ), (-σ)], I) → C''
117. Rotate(A'_{1}, If[4 < o ≤ 5, ((-(o - 4)) * σ), (-σ)], I) → U
118. Segment(C'', U) → s_3
119. Segment(A, S) → t_3
120. Segment(S, I) → a_3
121. Rotate(C'', If[5 < o ≤ 6, ((o - 5) * pi), pi], S) → C'''
122. Rotate(U, If[5 < o ≤ 6, ((o - 5) * pi), pi], S) → U'
123. Segment(C''', U') → b_3
124. Angle(I, A, M) → τ
125. Rotate(U', If[7 < o ≤ 8, ((o - 7) * τ), τ], A) → U''
126. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], M) → A'_{2}
127. Vector(A, A'_{2}) → v
128. Translate(A, v) → A'_{3}
129. Translate(D, v) → D'_{1}
130. Segment(A'_{3}, D'_{1}) → g'
131. Segment(M, T) → c_3
132. Segment(T, A) → d_3
133. Line(M, A) → e_3
134. Point(e_3) → V
135. Angle(D, A, V) → χ
136. Rotate(A'_{3}, If[8 < o ≤ 9, ((o - 8) * χ), χ], M) → W
137. Rotate(D'_{1}, If[8 < o ≤ 9, ((o - 8) * χ), χ], M) → Z
138. Segment(W, Z) → g''
139. Rotate(W, If[9 < o ≤ 10, ((o - 9) * pi), pi], Z) → W'
140. Rotate(Z, If[9 < o ≤ 10, ((o - 9) * pi), pi], Z) → Z'
141. Segment(W', Z') → g'''
142. Polygon(A, B, C) → t2, c_4, a_4, b_4
143. Polygon(A, C, D) → t3, d_4, a_5, c_5
144. Polygon(A, D, E) → t4, e_4, a_6, d_5
145. OrthogonalLine(R, l_2) → f_4
146. Circle(R, 1) → g_4
147. Intersect(g_4, f_4, 2) → A_1
148. Segment(A, A_1) → h_4
149. Segment(A_1, R) → i_4
150. Angle(A_1, R, A) → υ
151. Circle(A, Distance[A, C]) → k_4
152. Intersect(k_4, h_4, 1) → B_1
153. Circle(B_1, Distance[A, C]) → p_4
154. Intersect(p_4, h_4, 2) → C_1
155. Segment(A, B_1) → j_4
156. Segment(B_1, C_1) → l_4
157. Segment(C_1, A_1) → m_4
158. Polygon(A, H, I) → t5, i_5, a_7, h_5
159. Polygon(A, L, M) → t6, m_5, a_8, l_5
160. Line(A_1, A) → n_4
161. Point(n_4) → D_1
162. Angle(C, A, D_1) → ϕ
163. Dilate(A, If[11 < o ≤ 12, 12 - o, 0], C_1) → A'_{4}
164. Vector(A, A'_{4}) → w
165. Translate(C, w) → C'_{2}
166. Translate(A, w) → A'_{5}
167. Segment(C'_{2}, A'_{5}) → q_4
168. Angle(A_1, A'_{4}, C'_{2}) → ψ
169. Rotate(C'_{2}, If[12 < o ≤ 13, ((o - 12) * ϕ), ϕ], C_1) → E_1
170. Rotate(A'_{5}, If[12 < o ≤ 13, ((o - 12) * ϕ), ϕ], C_1) → F_1
171. Segment(E_1, F_1) → r_4
172. Rotate(E_1, If[13 < o ≤ 14, ((-(o - 13)) * pi), (-pi)], A'_{5}) → G_1
173. Rotate(F_1, If[13 < o ≤ 14, ((-(o - 13)) * pi), (-pi)], A'_{5}) → H_1
174. Segment(G_1, H_1) → s_4
175. Rotate(E_1, If[14 < o ≤ 15, ((o - 14) * pi), pi], E_1) → I_1
176. Rotate(F_1, If[14 < o ≤ 15, ((o - 14) * pi), pi], E_1) → J_1
177. Segment(I_1, J_1) → t_4
178. RotateText(text12, atand(Slope[l_4])) → text13