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等差数列可视化

等差数列可视化
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2016-08-12 04:19
向量数列几何作图
①本范例通过动态演示等差数列的几何表示，直观展示数列项与首项、公差的关系；②涉及核心数学概念包括等差数列、向量、几何变换；③作图要点运用了Intersect, Point, Polygon, Vector, Sequence, Stretch, Translate等GeoGebra命令与对象，实现数列项的生成与变换；④适合高中数学教学，用于理解数列与几何图形的关联，提升空间想象能力。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → D
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Vector((0, 1)) → Up
  6. Vector((1, 0)) → Right
  7. Sequence(Sequence[Polygon[Translate[A, Vector[(Right * k) + (Up * m)]], Translate[B, Vector[(Right * k) + (Up * m)]], Translate[C, Vector[(Right * k) + (Up * m)]], Translate[D, Vector[(Right * k) + (Up * m)]]], k, 0, N - m - 1], m, 0, N) → list1
  8. Vector((StretchShrink, 0)) → StretchVector
  9. Stretch(list1, StretchVector) → stretchlist1
  10. Translate(stretchlist1, Vector[(10 * Right)]) → stretchlist2
  11. Vector((Shift, 0)) → ShiftVector
  12. Stretch(A, ShiftVector) → A'
  13. Stretch(B, ShiftVector) → B'
  14. Stretch(C, ShiftVector) → C'
  15. Stretch(D, ShiftVector) → D'
  16. Polygon(A', B', C', D') → AddOn, a', b', c', d'
  17. Translate(A', (10, -8)) → A''
  18. Translate(B', (10, -8)) → B''
  19. Translate(C', (10, -8)) → C''
  20. Translate(D', (10, -8)) → D''
  21. Polygon(A'', B'', C'', D'') → AddOn2, a'', b'', c'', d''
  22. Translate(stretchlist2, (Shift, (-8))) → ShiftList2
  23. Sequence(Polygon[Translate[A'', Vector[(Up * p)]], Translate[B'', Vector[(Up * p)]], Translate[C'', Vector[(Up * p)]], Translate[D'', Vector[(Up * p)]]], p, 0, N - 1) → ShiftList1