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立方体上的三角形

立方体上的三角形
几何画板及绘图内容加载中，请稍等……
2017-07-19 13:57
解析几何立体几何几何作图
①本范例演示如何在立方体表面构建三角形；②涉及核心数学概念包括立体几何、几何作图、向量与坐标几何；③构造过程中运用了点、立方体、点在对象内判断、旋转、线段、交点、条件判断等GeoGebra命令与对象；④适合高中及以上学生用于学习空间几何与几何作图方法。

GeoGebra 命令及参数

  1. Point(Circle[B_2, Distance[A_2, B_2], Segment[A_2, B_2]]) → C_2
  2. Cube(A_2, B_2, C_2) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. PointIn(faceEFGH) → B
  4. PointIn(faceABFE) → A
  5. PointIn(faceCDHG) → C
  6. Rotate(B, 90°, edgeEF) → I'
  7. Segment(A, I') → f
  8. Intersect(f, edgeEF) → L
  9. Rotate(B, 90°, edgeFG) → I'_1
  10. Rotate(A, (-(90°)), edgeBF) → J'
  11. Segment(I'_1, J') → g
  12. Intersect(g, edgeFG) → M
  13. Intersect(g, edgeBF) → N
  14. Rotate(C, 90°, edgeCG) → K'
  15. Segment(J', K') → i
  16. Rotate(C, (-(90°)), edgeGH) → K'_1
  17. Rotate(C, 90°, edgeDH) → K'_2
  18. Rotate(C, 90°, edgeCD) → K'_3
  19. Rotate(A, -90°, edgeEF) → J'_1
  20. Rotate(A, 90°, edgeAB) → J'_2
  21. Rotate(A, 90°, edgeAE) → J'_3
  22. Segment(J'_1, K'_1) → j
  23. Segment(J'_3, K'_2) → k
  24. Segment(J'_2, K'_3) → l
  25. Intersect(i, edgeBF) → O
  26. Intersect(i, edgeCG) → P
  27. Intersect(edgeEF, j) → Q
  28. Intersect(edgeGH, j) → R
  29. Intersect(edgeDH, k) → S
  30. Intersect(k, edgeAE) → T
  31. Intersect(edgeCD, l) → U
  32. Intersect(edgeAB, l) → V
  33. If(ii, PolyLine[A, O, P, C], If[ll, PolyLine[A, V, U, C], If[jj, PolyLine[A, Q, R, C], PolyLine[A, T, S, C]]]) → m
  34. Rotate(B, 90°, edgeGH) → I'_2
  35. Segment(C, I'_2) → n
  36. Rotate(B, 90°, edgeFG) → I'_3
  37. Rotate(C, 90°, edgeCG) → K'_4
  38. Segment(I'_3, K'_4) → p
  39. Rotate(C, 90°, edgeDH) → K'_5
  40. Rotate(B, 90°, edgeEH) → I'_4
  41. Segment(I'_4, K'_5) → q
  42. Intersect(edgeEH, q) → W
  43. Intersect(edgeDH, q) → Z
  44. Intersect(edgeGH, n) → A_1
  45. Intersect(p, edgeFG) → B_1
  46. Intersect(edgeCG, p) → C_1
  47. If(nn, PolyLine[C, A_1, B], If[pp, PolyLine[C, C_1, B_1, B], PolyLine[C, Z, W, B]]) → r
  48. Rotate(B, 90°, edgeEH) → I'_5
  49. Segment(I'_5, J'_3) → s
  50. Intersect(edgeEH, s) → D_1
  51. Intersect(edgeAE, s) → E_1
  52. If(ff, PolyLine[A, L, B], If[gg, PolyLine[A, N, M, B], PolyLine[A, E_1, D_1, B]]) → h