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部分整体矩形

部分整体矩形
几何画板及绘图内容加载中，请稍等……
2015-09-15 23:24
解析几何导数参数方程几何作图
①本范例演示了部分与整体关系的矩形分割与比较；②涉及核心数学概念包括解析几何、参数方程、导数及几何变换；③构造要点运用了Segment, Sequence, Point, Intersect, Polygon, If, Midpoint, OrthogonalLine, Textfield等命令及对象；④适合高中数学教学，用于理解函数、几何作图与参数方程的应用。

GeoGebra 命令及参数

  1. Segment(A, B) → c
  2. Sequence(Point[{((x(B) - x(A)) / 8 * i) + x(A), ((y(B) - y(A)) / 9 * i) + y(A)}], i, 0, 8, 1) → list1
  3. Point(list1) → bound1
  4. Point(list1) → bound2
  5. Intersect(xAxis, yAxis) → C
  6. Point(xAxis) → D
  7. Polygon(C, D, E, F) → poly1, c_1, d, e, f_1
  8. If(x(bound1) ≟ x(Element[list1, 1]), 10, If[x(bound1) ≟ x(Element[list1, 2]), 20, If[x(bound1) ≟ x(Element[list1, 3]), 50, If[x(bound1) ≟ x(Element[list1, 4]), 100, If[x(bound1) ≟ x(Element[list1, 5]), 200, If[x(bound1) ≟ x(Element[list1, 6]), 500, If[x(bound1) ≟ x(Element[list1, 7]), 1000, If[x(bound1) ≟ x(Element[list1, 8]), 5000, 10000]]]]]]]) → B1
  9. If(x(bound2) ≟ x(Element[list1, 1]), 10, If[x(bound2) ≟ x(Element[list1, 2]), 20, If[x(bound2) ≟ x(Element[list1, 3]), 50, If[x(bound2) ≟ x(Element[list1, 4]), 100, If[x(bound2) ≟ x(Element[list1, 5]), 200, If[x(bound2) ≟ x(Element[list1, 6]), 500, If[x(bound2) ≟ x(Element[list1, 7]), 1000, If[x(bound2) ≟ x(Element[list1, 8]), 5000, 10000]]]]]]]) → B2
  10. Midpoint(C, F) → G
  11. Midpoint(E, D) → H
  12. Point(Segment[G, H]) → I
  13. OrthogonalLine(I, e) → h
  14. Intersect(h, e) → J
  15. Intersect(h, c_1) → K
  16. Polygon(F, J, K, C) → poly2, f_2, j, k, c_2
  17. Midpoint(I, G) → textpoint
  18. Point(yAxis) → L
  19. Point(yAxis) → M
  20. Polygon(L, M, N, O) → poly3, l, m, n_2, o
  21. Point(yAxis) → P
  22. Point(yAxis) → Q
  23. Point(yAxis) → U
  24. Segment(P, Q) → i
  25. Segment(U, T) → p
  26. Segment(R, S) → q
  27. Polygon(L, (answerx, (-2)), (answerx, (-4)), M) → poly4, l_1, r, s, m_1
  28. Midpoint(Midpoint[L, M], (answerx, (-3))) → textpoint2
  29. Textfield(inTxt) → InputBox1
  30. Textfield(inTxt_3) → InputBox2