Geometric Construction Linking Logarithms and Definite Integrals (Task 6)

GeoGebra Commands & Parameters

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. Segment(C, D) → m_2
45. Segment(D, E) → n_2
46. Segment(E, F) → p_2
47. Segment(F, G) → q_2
48. Segment(G, H) → r_2
49. Segment(H, I) → s_2
50. Segment(I, J) → t_2
51. Segment(J, K) → a_2
52. Segment(K, L) → b_2
53. Segment(L, M) → f_3
54. Angle(C, B, A) → α
55. Angle(D, C, A) → β
56. Angle(E, D, A) → γ
57. Angle(F, E, A) → δ
58. Angle(G, F, A) → ε
59. Angle(H, G, A) → ζ
60. Angle(I, H, A) → η
61. Angle(J, I, A) → θ
62. Angle(K, J, A) → ι
63. Angle(L, K, A) → κ
64. Angle(M, L, A) → λ
65. Segment(A, B) → l_3
66. Segment(C, B) → m_3
67. Segment(C, A) → n_3
68. RotateText(text1_{1}, atand(Slope[n_3])) → text2
69. RotateText(text3, atand(Slope[g])) → text4
70. Midpoint(f_1) → S
71. Midpoint(n_1) → T
72. RotateText(text5, pi / 4) → text6
73. RotateText(text7, atan(Slope[g])) → text8
74. RotateText(text9, atand(Slope[i])) → text10
75. Rotate(D, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → D'
76. Rotate(E, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → E'
77. Segment(D', E') → p_3
78. Rotate(D', If[1 < o ≤ 2, ((-(o - 1)) * pi), (-pi)], D') → D''
79. Rotate(E', If[1 < o ≤ 2, ((o - 1) * pi), pi], D') → E''
80. Segment(D'', E'') → q_3
81. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], I) → A'
82. Vector(A, A') → u
83. Translate(C, u) → C'
84. Translate(A, u) → A'_{1}
85. Segment(C', A'_{1}) → r_3
86. Translate(C, u) → C'_{1}
87. Angle(A, I, C'_{1}) → σ
88. Rotate(C', If[4 < o ≤ 5, ((-(o - 4)) * σ), (-σ)], I) → C''
89. Rotate(A'_{1}, If[4 < o ≤ 5, ((-(o - 4)) * σ), (-σ)], I) → U
90. Segment(C'', U) → s_3
91. Segment(A, S) → t_3
92. Segment(S, I) → a_3
93. Rotate(C'', If[5 < o ≤ 6, ((o - 5) * pi), pi], S) → C'''
94. Rotate(U, If[5 < o ≤ 6, ((o - 5) * pi), pi], S) → U'
95. Segment(C''', U') → b_3
96. Angle(I, A, M) → τ
97. Rotate(U', If[7 < o ≤ 8, ((o - 7) * τ), τ], A) → U''
98. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], M) → A'_{2}
99. Vector(A, A'_{2}) → v
100. Translate(A, v) → A'_{3}
101. Translate(D, v) → D'_{1}
102. Segment(A'_{3}, D'_{1}) → g'
103. Segment(M, T) → c_3
104. Segment(T, A) → d_3
105. Line(M, A) → e_3
106. Point(e_3) → V
107. Angle(D, A, V) → χ
108. Rotate(A'_{3}, If[8 < o ≤ 9, ((o - 8) * χ), χ], M) → W
109. Rotate(D'_{1}, If[8 < o ≤ 9, ((o - 8) * χ), χ], M) → Z
110. Segment(W, Z) → g''
111. Rotate(W, If[9 < o ≤ 10, ((-(o - 9)) * pi), (-pi)], Z) → W'
112. Rotate(Z, If[9 < o ≤ 10, ((o - 9) * pi), pi], Z) → Z'
113. Segment(W', Z') → g'''
114. Polygon(A, B, C) → t2, c_4, a_4, b_4
115. Polygon(A, C, D) → t3, d_4, a_5, c_5
116. Polygon(A, D, E) → t4, e_4, a_6, d_5
117. Circle(A, Distance[A, C]) → k_4
118. Polygon(A, H, I) → t5, i_5, a_7, h_5
119. Polygon(A, L, M) → t6, m_5, a_8, l_5
120. RotateText(text12, atand(Slope[c_3] + pi / 2)) → text13
121. RotateText(text13, pi) → text14