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长方体展开图 by Ooi Soo Huat

长方体展开图 by Ooi Soo Huat
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2018-01-08 15:15
多边形立体几何几何作图
所属专题 Mathematics Form 2 Nets of Solid Figures (Primary 6)
①本范例演示长方体(cuboid)的不同展开图 nets；②涉及核心数学概念：立体几何、多边形、几何变换；③作图要点：使用 GeoGebra 命令 If, Line, Rotate, SelectedIndex 构造长方体及其展开图，通过变换展示不同展开方式；④适合初中及以上学生学习立体几何、空间想象能力及几何作图。

GeoGebra 命令及参数

  1. If(o ≟ 3 ∨ o ≟ 7, N03, o ≟ 4, N04, o ≟ 11, N11, N03) → N
  2. If(o ≟ 4, P04, o ≟ 11, P11, P04) → P
  3. If(o ≟ 11, J11, J01) → J
  4. If(o ≟ 11, H11, H01) → H
  5. If(o ≟ 11, Line[H, N], Line[G, H]) → h
  6. Line(A, B) → g
  7. Line(C, B) → i
  8. Rotate(g, ((d * 90))°, i) → l
  9. Rotate(Rotate[h, ((d * 90))°, i], ((-((d * 90))))°, l) → n
  10. Line(D, C) → f
  11. Rotate(f, ((d * 90))°, i) → f'
  12. If(o ≤ 4 ∨ o ≟ 9 ∨ o ≟ 10, I01, o ≟ 5 ∨ o ≟ 6, I05, I05) → I
  13. If(o ≟ 8, F08, F01) → F
  14. If(o ≟ 1, L01, o ≟ 2 ∨ o ≟ 6 ∨ o ≟ 8 ∨ o ≟ 9 ∨ o ≟ 11, L02, L01) → L
  15. If(o ≟ 1, K01, o ≟ 8, K08, K01) → K
  16. If(o ≟ 5, S05, S05) → S
  17. If(o ≟ 5, T05, T05) → T
  18. Line(D, A) → j
  19. Rotate(j, ((-((d * 90))))°, g) → j'
  20. If(o ≟ 5, R05, o ≟ 9 ∨ o ≟ 10, R09, R05) → R
  21. Rotate(Rotate[h, ((-((d * 90))))°, g], (((-d) * 90))°, j') → k
  22. Rotate(h, ((-((d * 90))))°, g) → h'
  23. If(o ≟ 2, M02, o ≟ 3 ∨ o ≟ 7 ∨ o ≟ 10, M03, M02) → M
  24. Rotate(Rotate[i, ((-((d * 90))))°, g], ((-((d * 90))))°, h') → i'_2
  25. If(o ≟ 9 ∨ o ≟ 10, Q09, Q01) → Q
  26. Rotate(i, ((d * 90))°, f) → i'
  27. Rotate(Polygon[A, B, C, D], ((d * 0))°, i) → ABCD
  28. Rotate(Polygon[D, C, F, E], ((d * 90))°, f) → DCFE'
  29. Rotate(Polygon[B, M, L, C], ((d * 90))°, i) → BMLC'
  30. Rotate(Polygon[R, A, D, Q], ((-((d * 90))))°, j) → RADQ'
  31. Rotate(Polygon[G, H, B, A], ((-((d * 90))))°, g) → GHBA'
  32. Rotate(Rotate[Polygon[C, L, K, F], ((d * 90))°, f], ((d * 90))°, i') → CLKF'
  33. Rotate(Rotate[Polygon[I, J, H, G], ((-((d * 90))))°, g], ((-((d * 90))))°, h') → IJHG'
  34. Rotate(i, ((-((d * 90))))°, g) → i'_1
  35. Rotate(Rotate[Rotate[Polygon[J, P, N, H], ((-((d * 90))))°, g], ((-((d * 90))))°, h'], ((d * 90))°, i'_2) → JPNH'
  36. Rotate(Rotate[Polygon[S, G, A, R], ((-((d * 90))))°, g], (((-d) * 90))°, j') → SGAR'
  37. Rotate(Rotate[Polygon[H, N, M, B], ((-((d * 90))))°, g], ((d * 90))°, i'_1) → HNMB'
  38. Rotate(j, ((d * 90))°, f) → j'_1
  39. Rotate(Rotate[Polygon[Q, D, E, U], ((d * 90))°, f], ((-((d * 90))))°, j'_1) → QDEU'
  40. Rotate(Rotate[Rotate[Polygon[T, I, G, S], ((-((d * 90))))°, g], ((-((d * 90))))°, j'], ((-((d * 90))))°, k) → TIGS'
  41. Rotate(Rotate[Polygon[C, L, K, F], ((d * 90))°, i], ((d * 90))°, f') → CLKF''
  42. Rotate(Rotate[Rotate[Polygon[J, P, N, H], ((d * 90))°, i], ((-((d * 90))))°, l], ((-((d * 90))))°, n) → JPNH''
  43. Rotate(Rotate[Polygon[H, N, M, B], ((d * 90))°, i], ((-((d * 90))))°, l) → HNMB''
  44. Rotate(Line[E, F], ((d * 90))°, f) → m
  45. Rotate(Rotate[Polygon[E, F, V, W], ((d * 90))°, f], ((d * 90))°, m) → EFVW'
  46. SelectedIndex(Bahasa) → nn
  47. Rotate(Prism[Polygon[A, B, C, D], c], 0°, i) → e