折纸制作纸盒

折纸制作纸盒
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2015-07-12 04:57
①本范例演示如何通过折纸将正方形纸片制作成立方体纸盒的过程;②涉及的核心数学概念包括多边形、立体几何、向量运算和几何变换;③作图要点提炼自构造摘要,使用了Point, Intersect, Midpoint, Segment, Circle, Line, OrthogonalLine, Mirror, Polygon, Prism, Vector等GeoGebra命令和对象;④适合高中阶段学生学习和理解空间几何与几何作图。

GeoGebra 命令及参数

  1. Point(xAxis) → F
  2. Intersect(xAxis, yAxis) → B
  3. Midpoint(B, F) → I
  4. Point(yAxis) → E
  5. Segment(B, E) → c
  6. Midpoint(B, E) → H
  7. Min(Distance[B, I], Distance[B, H]) → mRad
  8. Circle(B, mRad) → h
  9. Intersect(h, c) → J,
  10. Segment(B, J) → g
  11. Point(g) → K
  12. Distance(B, K) → Height
  13. Intersect(yAxis, zAxis) → O
  14. Line(A, yAxis) → a
  15. Line(C, xAxis) → b
  16. Intersect(a, b) → D
  17. Segment(B, F) → d
  18. OrthogonalLine(F, xAxis) → e
  19. OrthogonalLine(E, yAxis) → f
  20. Intersect(e, f) → G
  21. Mirror(K, H) → K'
  22. Mirror(K, i) → BR
  23. Mirror(BR, I) → L
  24. OrthogonalLine(I, xAxis) → j
  25. Mirror(K, j) → K'_2
  26. Mirror(K', j) → K''
  27. OrthogonalLine(H, c) → k
  28. Mirror(BR, k) → M
  29. Mirror(L, k) → L'
  30. Segment(E, G) → l
  31. Segment(G, F) → m
  32. Line(L, L') → n
  33. Line(M, BR) → p
  34. Line(K, K'_2) → q
  35. Line(K', K'') → r
  36. Intersect(p, r) → N
  37. Intersect(r, n) → P
  38. Intersect(n, q) → Q
  39. Intersect(q, p) → R
  40. Polygon(B, BR, R, K) → poly1, b_1, k'_1, r_1, k_1
  41. Polygon(L, F, K'_2, Q) → poly2, l_1, f_1, k'_2, q_1
  42. Polygon(P, K'', G, L') → poly3, p_1, k'', g_1, l'
  43. Polygon(K', N, M, E) → poly4, k', n_1, m_1, e_1
  44. Prism(O, A, D, C, V) → Volume, S, edgeAO, edgeAD, edgeCD, edgeCO, edgeOV, edgeAS, edgeDT, edgeCU, edgeSV, edgeST, T, edgeTU, edgeUV, U, faceADCO, faceAOVS, faceADTS, faceCDTU, faceCOVU, faceSTUV
  45. Distance(B, E) → w_O
  46. Distance(B, F) → l_O
  47. Intersect(s, xAxis) → Z, root2, B_1
  48. Polygon(K', K, M, N, R, BR, L, Q, K'_2, K'', P, L') → poly5, k'_3, l'_1, m_2, n_2, k_2, r_2, k'_4, l_2, q_2, k'_5, k''_1, p_2
  49. Midpoint(BL, BRL) → A_1
  50. Vector(BL, BRL) → u
  51. Vector(BRL, BL) → v
  52. Segment(W, (0, y(W))) → a_1
  53. Segment(W, (x(W), 0)) → c_1

AI 绘图提示语参考

绘制一个正方形纸张折叠成一个立方体盒子的过程。首先在x轴上取点F,在y轴上取点E,连接BE并取其中点H。以B为圆心,BH为半径画圆h,与BE交于J,连接BJ。接着构造正方形纸张的四个角点B、E、F、G,以及立方体的各个面和棱。最后通过镜像和旋转操作,形成完整的立方体盒子。
以上提示语为根据原始绘图命令整理而来,仅供参考。