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立方体与球表面积相等

立方体与球表面积相等
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2019-05-26 02:33
圆立体几何几何作图
①本范例演示立方体与球表面积相等的几何模型；②涉及核心数学概念包括立体几何、表面积计算、圆周率近似值；③作图要点：使用Point, Segment, Polygon, Line, Midpoint, Circle, Intersect, Semicircle, Distance, Rotate, Angle等GeoGebra命令构建几何图形；④适合高中数学教学，用于理解空间几何与圆周率关系的探索。

GeoGebra 命令及参数

  1. Point(Circle[A, 12]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
  4. Point(h) → E
  5. Point(h) → F
  6. Line(E, F) → k
  7. Midpoint(C, B) → G
  8. Circle(G, 13.41640786499874) → c
  9. Point(j) → H
  10. Line(H, I) → l
  11. Point(c) → J
  12. Circle(B, J) → d
  13. Intersect(d, l, 2) → K
  14. Segment(K, A) → m
  15. Midpoint(A, K) → L
  16. Midpoint(K, A) → M
  17. Circle(L, 4) → e
  18. Point(Circle[A, 4]) → N
  19. Segment(A, N) → n
  20. Polygon(N, A, 4) → poly2, p, q, r, s, O, P
  21. Segment(N, O) → t
  22. Semicircle(D, O) → c_1
  23. Distance(A, f) → distanceAf
  24. Intersect(c_1, f, 1) → Q
  25. Segment(A, Q) → a
  26. Distance(A, Q) → distanceAQ
  27. Circle(N, 6.821178167174472) → d_1
  28. Circle(A, 5.525257603798908) → e_1
  29. Intersect(d_1, e_1, 2) → R
  30. Segment(A, R) → b
  31. Midpoint(R, A) → S
  32. Circle(S, 2.762628801899454) → f_1
  33. Segment(N, R) → g_1
  34. Distance(A, R) → distanceAR
  35. Rotate(O, 45°, N) → O'
  36. Angle(O, N, O') → α
  37. Circle(O, 8) → h_1
  38. Intersect(h_1, l, 1) → T
  39. Polygon(T, O, 4) → poly3, i_1, j_1, k_1, l_1, U, V
  40. Segment(V, O) → m_1
  41. Polygon(P, O, 4) → poly4, n_1, p_1, q_1, r_1, W, Z
  42. Segment(P, W) → s_1
  43. Polygon(O, A, 4) → poly5, t_1, a_1, b_1, f_2, A_1, B_1
  44. Segment(A, B_1) → g_2
  45. Polygon(O, B_1, 4) → poly6, h_2, i_2, j_2, k_2, C_1, D_1