正多边形面积计算 by Tim Brzezinski

GeoGebra 命令及参数

1. Sequence((cos(((k * π) * β / 180)), sin(((k * π) * β / 180))), k, 0, NoSides, 1) → list1
2. Distance(Element[list1, 1], Element[list1, 2]) → h
3. Center(c) → A
4. Sequence(Polygon[Element[list1, k], A, Element[list1, k + 1]], k, 1, NoSides, 1) → list2
5. Sequence(Vertex[Element[list2, k], 3], k, 2, NoSides, 1) → list4
6. Sequence(Vertex[Element[list2, k], 3], k, 1, NoSides - 1) → list5
7. Rotate(A, (((-b) * 360) * ° / NoSides), B_1) → A'
8. Sequence(Rotate[Element[list1, k], ((((-(k - 1)) * b) * 360) * ° / NoSides), Element[list1, k - 1]], k, 2, NoSides, 1) → list3
9. Sequence(Rotate[Element[list3, k], ((((-(k - 1)) * b) * 360) * ° / NoSides), Element[list3, k - 1]], k, 2, NoSides - 1, 1) → list6
10. Polygon(Element[list1, 1], A', Element[list3, 1]) → poly1, d, e, a'
11. Vector(Element[list1, 2], Element[list3, 1]) → u
12. Sequence(Vector[Element[list1, k], Element[list3, k - 1]], k, 2, NoSides, 1) → list7
13. Segment((0, -1), (6.283185307179586, -1)) → f
14. Intersect(c, d, 1) → D
15. Segment(D, C) → i
16. Dilate(D, If[0 < g ≤ 1, 1 - g, 0], C) → D'
17. Vector(D, D') → v
18. Translate(list1, v) → list1'
19. Translate(c, v) → c'
20. Translate(list2, v) → list2'
21. Rotate(Element[list2', 1], (((-g) * 360 / NoSides))°, Element[list1', 1]) → poly2
22. Vertex(Element[list2', 2], 1) → E
23. Vertex(poly2, 3) → F
24. Vector(Vertex[Element[list2', 2], 1], Vertex[poly2, 3]) → w
25. Translate(Element[list2', 2], w) → poly3
26. Rotate(poly3, ((((-g) * 2) * 360 / NoSides))°, F) → poly3'
27. Vertex(poly3', 3) → G
28. Vector(Vertex[Element[list2', 3], 1], Vertex[poly3', 3]) → j
29. Translate(Element[list2', 3], j) → poly4
30. Rotate(poly4, ((((-g) * 3) * 360 / NoSides))°, G) → poly4'
31. Vertex(poly4', 3) → H
32. Vector(Element[list1', 4], H) → k
33. Translate(Element[list2', 4], k) → poly5
34. Rotate(poly5, ((((-g) * 4) * 360 / NoSides))°, H) → poly5'
35. Vertex(poly5', 3) → I
36. Vector(Element[list1', 5], I) → l
37. Translate(Element[list2', 5], l) → poly6
38. Rotate(poly6, ((((-g) * 5) * 360 / NoSides))°, I) → poly6'
39. Vertex(poly6', 3) → J
40. Vector(Element[list1', 6], J) → m
41. Translate(Element[list2', 6], m) → poly7
42. Rotate(poly7, ((((-g) * 6) * 360 / NoSides))°, J) → poly7'
43. Rotate(poly7, ((((-g) * 6) * 360 / NoSides))°, J) → poly7'_1
44. Vertex(poly7'_1, 3) → K
45. Vector(Element[list1', 7], K) → n
46. Translate(Element[list2', 7], n) → poly8
47. Rotate(poly8, ((((-g) * 7) * 360 / NoSides))°, K) → poly8'
48. Vertex(poly8', 3) → L
49. Vector(Element[list1', 8], L) → p
50. Translate(Element[list2', 8], p) → poly9
51. Rotate(poly9, ((((-g) * 8) * 360 / NoSides))°, L) → poly9'
52. Vertex(poly9', 3) → M
53. Vector(Element[list1', 9], M) → q
54. Translate(Element[list2', 9], q) → poly10
55. Vertex(poly2, 2) → B
56. Vertex(poly3', 2) → N
57. Vertex(poly4', 2) → O
58. Vertex(poly5', 2) → P
59. Vertex(poly6', 2) → Q
60. Vertex(poly7'_1, 2) → R
61. Vertex(poly8', 2) → S
62. Vertex(poly9', 2) → T
63. Rotate(poly2, (((-o) * 180))°, B) → poly2'
64. Rotate(poly3', (((-o) * 180))°, N) → poly3''
65. Rotate(poly4', (((-o) * 180))°, O) → poly4''
66. Rotate(poly5', (((-o) * 180))°, P) → poly5''
67. Rotate(poly6', (((-o) * 180))°, Q) → poly6''
68. Rotate(poly7'_1, (((-o) * 180))°, R) → poly11
69. Rotate(poly8', (((-o) * 180))°, S) → poly8''
70. Rotate(poly9', (((-o) * 180))°, T) → poly9''
71. Dilate(B, 1 - r, C) → B'
72. Dilate(N, 1 - r, F) → N'
73. Dilate(O, 1 - r, G) → O'
74. Dilate(P, 1 - r, H) → P'
75. Dilate(Q, 1 - r, I) → Q'
76. Dilate(R, 1 - r, J) → R'
77. Dilate(S, 1 - r, K) → S'
78. Dilate(T, 1 - r, L) → T'
79. Vector(N, N') → s
80. Vector(B, B') → t
81. Vector(O, O') → u_1
82. Vector(P, P') → v_1
83. Vector(Q, Q') → w_1
84. Vector(R, R') → a_1
85. Vector(S, S') → b_1
86. Vector(T, T') → c_1
87. Translate(poly2', t) → poly2''
88. Translate(poly3'', s) → poly3'''
89. Translate(poly4'', u_1) → poly4'''
90. Translate(poly5'', v_1) → poly5'''
91. Translate(poly6'', w_1) → poly6'''
92. Translate(poly11, a_1) → poly11'
93. Translate(poly8'', b_1) → poly8'''
94. Translate(poly9'', c_1) → poly9'''