Parabola Sketching with Isosceles Triangles via Geometric Construction

GeoGebra Commands & Parameters

1. Segment(A, B) → a
2. Rotate(B, (a_{2} * pi / 180), A) → B'
3. Ray(A, B') → f
4. Point(f) → C
5. Segment(A, C) → b
6. OrthogonalLine(C, b) → r
7. Circle(C, 1) → t
8. Intersect(t, r, 2) → K
9. OrthogonalLine(K, r) → i_1
10. Point(i_1) → W
11. Rotate(E, (a_{2} * pi / 180), D) → E'
12. Ray(D, E') → j
13. Segment(D, E) → a'
14. Circle(D, (a' / a * b)) → d
15. Intersect(d, j, 1) → F
16. Segment(D, F) → b'
17. Line(K, b') → k_1
18. Point(k_1) → U
19. Line(K, a') → j_1
20. Point(j_1) → V
21. Circle(B, 1) → s
22. OrthogonalLine(B, a) → q
23. Point(q) → M
24. Intersect(s, q, 1) → J
25. OrthogonalLine(J, q) → h_1
26. Point(h_1) → P
27. Polygon(A, B, C) → t1, c_{2}, a_1, b_{1}
28. Polygon(D, F, E) → t2, e, d_1, f_1
29. Min({a, a', b, b'}) → g
30. Circle(A, (0.35 * g)) → h
31. Intersect(h, a, 1) → G
32. Intersect(h, b, 1) → H
33. CircleSector(A, G, H) → k
34. Line(A, a') → i
35. Dilate(A, If[-1 < l ≤ 0, (-l), 0], D) → A'
36. Vector(A, A') → u
37. Translate(k, u) → k'
38. Point(i) → I
39. Angle(I, A, B) → α
40. CircleArc(A, G, H) → p
41. Dilate(D, If[1 < l ≤ 2, 2 - l, 0], J) → D'
42. Vector(D, D') → v
43. Translate(D, v) → D'_{1}
44. Translate(E, v) → E'_{1}
45. Segment(D'_{1}, E'_{1}) → a''
46. Line(J, a') → g_1
47. Point(g_1) → L
48. Angle(P, J, L) → β
49. Rotate(D'_{1}, If[1 < l ≤ 2, ((l - 1) * β), β], D'_{1}) → N
50. Rotate(E'_{1}, If[1 < l ≤ 2, ((-(l - 1)) * β), (-β)], D'_{1}) → O
51. Segment(N, O) → a'''
52. Dilate(D, If[2 < l ≤ 3, 3 - l, 0], K) → D'_{2}
53. Vector(D, D'_{2}) → w
54. Translate(D, w) → D'_{3}
55. Translate(E, w) → E'_{2}
56. Point(j_1) → Q
57. Point(i_1) → R
58. Angle(W, K, U) → γ
59. Rotate(D'_{3}, If[2 < l ≤ 3, ((l - 2) * γ), γ], D'_{3}) → S
60. Rotate(E'_{2}, If[2 < l ≤ 3, ((l - 2) * γ), γ], D'_{3}) → T
61. Translate(D, w) → D'_{4}
62. Translate(F, w) → F'
63. Segment(D'_{4}, F') → b''
64. Rotate(D'_{4}, If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], K) → Z
65. Rotate(F', If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], K) → F''
66. Segment(Z, F'') → b'''
67. Angle(A, C, B) → δ
68. Intersect(t, b, 1) → A_1
69. Rotate(A_1, If[-3 < l ≤ -2, ((l + 3) * δ), δ], C) → B_1
70. CircleSector(C, A_1, B_1) → e_1
71. Dilate(C, If[-1 < l ≤ 0, (-l), 0], F) → C'
72. Vector(C, C') → u_1
73. Translate(e_1, u_1) → p_1
74. Line(C, b') → l_1
75. Point(l_1) → C_1
76. Angle(C_1, C, A) → ε
77. Segment(F, E) → m_1
78. Segment(B, C) → c
79. OrthogonalLine(B, c) → r_1
80. Circle(B, 1) → s_1
81. Intersect(s_1, r_1, 1) → D_1
82. Dilate(E, If[3 < l ≤ 4, 4 - l, 0], D_1) → E'_{3}
83. Vector(E, E'_{3}) → v_1
84. Translate(F, v_1) → F'_{1}
85. Translate(E, v_1) → E'_{4}
86. Segment(F'_{1}, E'_{4}) → t_1
87. Line(E, c) → f_2
88. Point(f_2) → E_1
89. Angle(F, E, E_1) → ζ
90. Rotate(F'_{1}, If[3 < l ≤ 4, ((l - 3) * ζ), ζ], E'_{3}) → F_1
91. Rotate(E'_{4}, If[3 < l ≤ 4, ((l - 3) * ζ), ζ], E'_{3}) → G_1
92. Segment(F_1, G_1) → g_2
93. Angle(B, A, C) → η
94. Rotate(G, If[-3 < l ≤ -2, ((l + 3) * η), η], A) → G'
95. CircleSector(A, G, G') → d_2
96. CircleArc(C, A_1, B_1) → e_2
97. Rotate(p_1, If[-1 < l ≤ 0, ((-(l + 1)) * ε), (-ε)], C') → q_1
98. Rotate(k', If[-1 < l ≤ 0, ((-(l + 1)) * α), (-α)], A') → k''