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嵌套与旋转的立方体 by Steve Phelps

嵌套与旋转的立方体 by Steve Phelps
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2017-10-09 22:00
数列立体几何变换
①本范例演示了立方体嵌套与旋转的动态效果；②涉及核心数学概念包括立体几何、变换、数列等；③构造中使用了点、立方体、序列等 GeoGebra 命令与对象；④适合高中及以上学生及数学爱好者用于理解空间几何与变换。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → 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. Sequence(Dilate[Rotate[Rotate[Rotate[a, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L
  4. Sequence(Dilate[Rotate[Rotate[Rotate[A, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_1
  5. Sequence(Dilate[Rotate[Rotate[Rotate[B, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_2
  6. Sequence(Dilate[Rotate[Rotate[Rotate[C, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_3
  7. Sequence(Dilate[Rotate[Rotate[Rotate[D, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_4
  8. Sequence(Dilate[Rotate[Rotate[Rotate[E, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_5
  9. Sequence(Dilate[Rotate[Rotate[Rotate[F, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_6
  10. Sequence(Dilate[Rotate[Rotate[Rotate[G, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_7
  11. Sequence(Dilate[Rotate[Rotate[Rotate[H, (i * π / 72), yAxis], (i * π / 72), zAxis], (i * π / 72), xAxis], 0.92^(i)], i, 1, n) → L_8