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五棱锥展开图

五棱锥展开图
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2012-04-27 00:13
多边形立体几何几何作图
①本范例演示五棱锥的展开图及其相关几何性质；②涉及核心数学概念包括多边形、立体几何、中点、距离、向量等；③作图要点运用了Segment、OrthogonalLine、Point、Intersect、Polygon、Midpoint、Perimeter、Distance、Vector、Translate等GeoGebra命令与对象；④适合高中阶段学习立体几何的学生使用，有助于理解多面体的展开与重构。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Polygon(A, C, D, B) → poly1, PrismHeight, c_1, d_1, b_1
  8. Polygon(A, B, 5) → BaseArea, e, f, g, i, m, E, N, O
  9. Midpoint(D, C) → H
  10. OrthogonalLine(H, c_1) → h
  11. Point(h) → I
  12. Perimeter(BaseArea) → perimeterpoly2
  13. Midpoint(A, B) → J
  14. Distance(I, J) → distanceIJ
  15. Perimeter(BaseArea) → k
  16. LaTeX(PRISmVolume, true, true) → text2
  17. LaTeX(PyramidVolume, true, true) → text3
  18. LaTeX(PrismHeight, true, true) → text1
  19. Distance(B, A) → distanceBA
  20. Polygon(A, B, I) → poly2, BaseSideLength, a_1, b_3
  21. Circle(K, a) → p
  22. Perimeter(poly1) → perimeterpoly1
  23. Perimeter(poly1) → n
  24. Perimeter(poly1) → o
  25. Point(PrismHeight) → F
  26. Line(F, c_1) → j
  27. Intersect(j, d_1) → G
  28. Distance(G, F) → distanceGF
  29. Circle(K, distanceGF) → q
  30. Line(K, j) → l
  31. Intersect(q, l) → L, M
  32. Vector(K, L) → u
  33. Vector(K, M) → v
  34. Distance(A, B) → distanceAB
  35. LaTeX(BaseSideLength, true, true) → text5
  36. LaTeX(pyramidHeight, true, true) → text6
  37. Translate(A, u) → A'
  38. Translate(B, u) → B'
  39. Translate(I, u) → I'
  40. Polygon(A', B', I') → poly2', i', a', b'
  41. Translate(A', u) → A''
  42. Translate(B', u) → B''
  43. Translate(I', u) → I''
  44. Polygon(A'', B'', I'') → poly2'', i'', a'', b''
  45. Translate(A, v) → A'_1
  46. Translate(B, v) → B'_1
  47. Translate(I, v) → I'_1
  48. Polygon(A'_1, B'_1, I'_1) → poly2'_1, i'_1, a'_1, b'_1
  49. Translate(A'_1, v) → P
  50. Translate(B'_1, v) → Q
  51. Translate(I'_1, v) → R
  52. Polygon(P, Q, R) → poly3, r, p_1, q_1