椭圆与多边形几何构造及向量变换范例

GeoGebra 命令及参数

1. OrthogonalLine(C, xAxis) → z2
2. Circle(C, 0.62) → z0
3. Intersect(z0, z2, 1) → Z4
4. Intersect(z0, z2, 2) → Z3
5. Ellipse(Z3, Z4, 0.65) → zElipse2
6. Point(zElipse2) → Z
7. Intersect(zElipse2, z2) → Z7, Z8
8. Angle(Z8, C, Z) → zAngInc
9. OrthogonalLine(C, yAxis) → z1
10. Intersect(z0, z1, 2) → Z2
11. Intersect(z0, z1, 1) → Z1
12. Ellipse(Z1, Z2, 0.65) → zElipse1
13. Point(zElipse1) → XY
14. Translate((0, 0), v) → O
15. OrthogonalLine(O, yAxis) → d
16. Point(d) → G
17. Vector((0, 0), G) → w
18. Sequence(PuntoEsfera[C, XY, Z, radio, 0, (s * α)], s, 0, n) → puntosA
19. Sequence((x(w) + x(Element[puntosA, s]), y(w) + y(Element[puntosA, s])), s, 1, n + 1) → puntosB
20. Sequence(Segment[Element[puntosB, s], Element[puntosA, s]], s, 1, n) → aristas
21. Element(aristas, 4) → a4
22. Point(a4) → E
23. Element(aristas, 3) → a3
24. Point(a3) → D
25. Element(aristas, 2) → a2
26. Point(a2) → B
27. Element(aristas, 1) → a1
28. Point(a1) → A
29. Element(puntosB, 4) → B4
30. Element(puntosB, 3) → B3
31. Element(puntosB, 2) → B2
32. Element(puntosB, 1) → B1
33. Intersect(zElipse1, z1) → Z5, Z6
34. Segment(Z5, Z6) → z4
35. Segment(Z7, Z8) → z3
36. Intersect(zElipse2, zElipse1, 1) → zPunto1
37. Intersect(zElipse2, zElipse1, 4) → zPunto2
38. Segment(zPunto1, zPunto2) → zSeg2
39. Polygon(B1, B2, B3, B4) → poly2, a, b, c, e
40. Angle(Z6, C, XY) → zAngRot
41. Sequence(Angle[Element[puntosB, s + 1], Element[puntosB, s], Element[puntosA, s + 1]], s, 1, n) → angulos
42. Sequence(If[s > 1 ∧ Element[angulos, s - 1] > 180° ∧ Element[angulos, s] > 180°, false, If[s ≟ 1 ∧ Element[angulos, n] > 180° ∧ Element[angulos, s] > 180°, false, true]], s, 1, n) → aristasVisibles
43. Element(aristas, 1) → a1b
44. Element(aristas, 2) → a2b
45. Polygon(A, B, D, E) → poly1, f, g, h, i
46. Element(aristas, 3) → a3b
47. Sequence(If[Element[angulos, s] > 180°, false, true], s, 1, n) → carasVisibles
48. Angle(B1, B2, B3) → β
49. Element(aristas, 4) → a4b
50. Polygon(A, D, B) → poly3, b_1, a_1, d_1
51. Polygon(B1, B3, B2) → poly4, b2, b1, b3
52. Polygon(B1, A, D, B3) → poly5, b1_1, a_2, d_2, b3_1
53. Midpoint(A, D) → I
54. Angle(H, I, F) → γ
55. Midpoint(e) → J
56. Midpoint(a) → K
57. Midpoint(b) → L
58. Midpoint(c) → M
59. Midpoint(h) → N
60. Midpoint(g) → P
61. Midpoint(f) → Q
62. Midpoint(i) → R
63. Segment(A, D) → j
64. Midpoint(J, K) → S
65. Midpoint(M, L) → T
66. Line(S, a2) → k
67. Line(T, a2) → l
68. Intersect(j, k) → U
69. Intersect(j, l) → V
70. Segment(S, U) → m
71. Segment(T, V) → p
72. Polygon(R, U, V, N) → poly6, r, u_1, v_1, n_1
73. Polygon(U, Q, P, V) → poly7, u_2, q, p_1, v_2
74. Polygon(J, S, T, M) → poly8, j_1, s, t, m_1
75. Polygon(S, K, L, T) → poly9, s_1, k_1, l_1, t_1
76. Polygon(J, R, N, M) → poly10, j_2, r_1, n_2, m_2
77. Polygon(K, Q, P, L) → poly11, k_2, q_1, p_2, l_2