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立方体中的缝合线

立方体中的缝合线
几何画板及绘图内容加载中，请稍等……
2016-03-05 18:51
解析几何立体几何几何作图
这个范例演示了立方体中缝合线的分析。涉及的核心数学概念包括立体几何中的面和边。通过使用GeoGebra命令如Point、Cube、Intersect等，构建了立方体的各个面和边。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Point(Circle[B_1, Distance[A, B_1], Segment[A, B_1]]) → C_1
  2. Cube(A, B_1, C_1) → a, D_1, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E_1, edgeBF, edgeFG, edgeCG, edgeGH, F_1, G_1, H_1, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Circle(xAxis, G_1) → c
  4. Intersect(zAxis, c) → I, J
  5. CircleArc(A, G_1, I) → d
  6. Point(d) → G
  7. Angle(G_1, A, G) → α
  8. Line(G, A) → b
  9. Rotate(a, α, xAxis) → a'
  10. Rotate(B_1, α, xAxis) → B
  11. Rotate(C_1, α, xAxis) → C
  12. Rotate(D_1, α, xAxis) → D
  13. Rotate(E_1, α, xAxis) → E
  14. Rotate(F_1, α, xAxis) → F
  15. Rotate(H_1, α, xAxis) → H
  16. Segment(A, B) → e
  17. Segment(B, C) → f
  18. Segment(C, D) → g
  19. Segment(D, A) → h
  20. Segment(E, F) → i
  21. Segment(F, G) → j
  22. Segment(H, E) → l
  23. Segment(E, A) → m
  24. Segment(F, B) → n
  25. Segment(G, C) → p_1
  26. Segment(H, D) → q
  27. Sequence(C + (k * (B - C)), k, 0, 1, 0.1) → CB
  28. Sequence(F + (k * (E - F)), k, 0, 1, 0.1) → FE
  29. Sequence(H + (k * (D - H)), k, 0, 1, 0.1) → HD
  30. Sequence(Segment[Element[CB, k], Element[FE, k]], k, 1, 11) → list1
  31. Sequence(Segment[Element[FE, k], Element[HD, k]], k, 1, 11) → list2
  32. Sequence(Segment[Element[HD, k], Element[CB, k]], k, 1, 11) → list3
  33. Polygon(Element[CB, p], Element[FE, p], Element[HD, p]) → poly1, r, s, t
  34. Segment(H, G) → k
  35. Vector(C, C + ((p - 1) / 10 * (B - C))) → u
  36. Vector(F, F + ((p - 1) / 10 * (E - F))) → v
  37. Vector(H, H + ((p - 1) / 10 * (D - H))) → w