正方体截面练习

正方体截面练习
几何画板及绘图内容加载中,请稍等……
2012-03-02 17:37
①本范例演示如何通过动态交互展示正方体不同角度的截面形状;②涉及的核心数学概念包括立体几何、几何作图、空间想象及不等式表示;③作图要点提炼自构造摘要,使用了Circle(圆)、PointIn(点在路径上)、Sequence(序列)、Element(元素)、Polygon(多边形)、Segment(线段)、Corner(角点)、Line(直线)、Intersect(交点)等GeoGebra命令与对象;④适合高中立体几何教学,用于加深学生对三维图形截面变化的理解与探究。

GeoGebra 命令及参数

  1. Circle(K_1, L) → c
  2. PointIn(c) → P
  3. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  4. Element(Element[AE, 3], 1) → droite_1
  5. Sequence(O + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  6. Element(listepoints, 3) → C
  7. Element(AB, 3, 1) → avant_1
  8. Element(AC, 3, 1) → dessus_1
  9. Element(listepoints, 4) → D
  10. Element(listepoints, 8) → H
  11. Element(listepoints, 7) → G
  12. Polygon(D, H, G, C) → dessus, s_{DHdessus}, s_{HGdessus}, s_{GCdessus}, s_{CDdessus}
  13. Element(listepoints, 1) → A
  14. Element(listepoints, 5) → E
  15. Polygon(D, A, E, H) → arrière, s_{DAarrière}, s_{EAarrière}, s_{EHarrière}, s_{HDarrière}
  16. Element(listepoints, 6) → F
  17. Polygon(H, G, F, E) → droite, s_{HGdroite}, s_{GFdroite}, s_{EFdroite}, s_{EHdroite}
  18. Element(listepoints, 2) → B
  19. Polygon(D, C, B, A) → gauche, s_{CDgauche}, s_{BCgauche}, s_{BAgauche}, s_{ADgauche}
  20. Polygon(F, B, C, G) → avant, s_{FBav}, s_{BCavant}, s_{CGavant}, s_{GFavant}
  21. Polygon(B, F, E, A) → dessous, s_{BFdessous}, s_{FEdessous}, s_{EAdessous}, s_{ABdessous}
  22. Segment(B, A) → p_{AB}
  23. Segment(D, C) → p_{DC}
  24. Segment(H, G) → p_{HG}
  25. Segment(G, F) → p_{GF}
  26. Segment(A, D) → p_{AD}
  27. Segment(E, H) → p_{HE}
  28. Segment(F, E) → p_{FE}
  29. Segment(A, E) → p_{EA}
  30. Segment(F, B) → p_{FB}
  31. Segment(H, D) → p_{HD}
  32. Segment(E, H) → p_{EH}
  33. Segment(C, G) → p_{CG}
  34. Segment(C, B) → p_{CB3}
  35. Segment(A, E) → p_{AE}
  36. Segment(C, B) → p_{CB}
  37. Corner(1) → coin1'
  38. Point(s_{BAgauche}) → I
  39. Point(s_{EAarrière}) → J
  40. Point(s_{CDgauche}) → K
  41. Segment(I, K) → a
  42. Segment(I, J) → b
  43. Line(K, b) → d
  44. Intersect(d, s_{HDarrière}) → O_1
  45. Segment(J, O_1) → e
  46. Intersect(d, p_{HG}) → Q
  47. Segment(J, Q) → f
  48. Polygon(I, J, Q, K) → poly1, j, m, q, n
  49. Polygon(I, J, O_1, K) → poly2, j_1, m_1, o, n_1
  50. Polygon(I, E, Q, K) → poly3, i, e_1, q_1, k
  51. Polygon(B, A, D, C) → poly4, b_1, a_1, d_1, c_1

AI 绘图提示语参考

绘制一个立方体,并展示其从不同角度的截面形状。首先绘制一个立方体,然后通过选择立方体的顶点和面,创建多个截面,包括前、后、上、下、左、右以及对角面。最后,连接这些截面的顶点,形成多个多边形,展示立方体在不同截面下的形状。
以上提示语为根据原始绘图命令整理而来,仅供参考。