测量二维图形面积 by GeoGebra Institute of Hong Kong

测量二维图形面积 by GeoGebra Institute of Hong Kong
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2014-12-10 09:06
所属专题 P4 Area (I)
①本范例演示如何通过数方格的方法测量二维图形的面积;②涉及的核心数学概念包括面积计算、算术平均、梯形、集合论、二次方程和勾股定理;③作图要点——从下方『构造摘要』提炼用到了Segment(线段)、Vector(向量)、Translate(平移)、Polygon(多边形)等GeoGebra命令和对象;④适合初中及以上学生学习和理解图形面积计算方法,也可用于数学教学演示。

GeoGebra 命令及参数

  1. Segment(X0, X0 + (0, 0.25)) → g
  2. Segment(X0, X0 + (0, mark)) → h
  3. Segment(X0 + (1, 0), X0 + (1, mark)) → i
  4. Vector(X0 + (0, mark / 2), X0 + (1, mark / 2)) → u
  5. Vector(X0 + (1, mark / 2), X0 + (0, mark / 2)) → v
  6. Segment(Y0 - (mark, 0), Y0) → j
  7. Segment(Y0 - (mark, 1), Y0 - (0, 1)) → k
  8. Vector(Y0 - (mark / 2, 1), Y0 - (mark / 2, 0)) → w
  9. Vector(Y0 - (mark / 2, 0), Y0 - (mark / 2, 1)) → z
  10. Segment((3, -1), (3, 3)) → l
  11. Translate(A, Vector[(t1 * Vector[A, D])]) → A'
  12. Translate(B, Vector[(t1 * Vector[A, D])]) → B'
  13. Translate(E, Vector[(t1 * Vector[A, D])]) → E'
  14. Polygon(A', B', E') → poly1, e', a', b'
  15. Translate(B, Vector[(t2 * Vector[B, A])]) → B'_1
  16. Translate(C, Vector[(t2 * Vector[B, A])]) → C'
  17. Translate(E, Vector[(t2 * Vector[B, A])]) → E'_1
  18. Polygon(B'_1, C', E'_1) → poly2, e'_1, b'_1, c'
  19. Translate(C, Vector[(t3 * Vector[D, A])]) → C'_1
  20. Translate(D, Vector[(t3 * Vector[D, A])]) → D'
  21. Translate(E, Vector[(t3 * Vector[D, A])]) → E'_2
  22. Polygon(C'_1, D', E'_2) → poly3, e'_2, c'_1, d'
  23. Translate(D, Vector[(t4 * Vector[A, B])]) → D'_1
  24. Translate(E, Vector[(t4 * Vector[A, B])]) → E'_3
  25. Translate(A, Vector[(t4 * Vector[A, B])]) → A'_1
  26. Polygon(D'_1, E'_3, A'_1) → poly4, a'_1, d'_1, e'_3
  27. Polygon(A', B', E') → poly1', e'_4, a'_2, b'_2
  28. Polygon(B'_1, C', E'_1) → poly2', e'_5, b'_3, c'_2
  29. Polygon(C'_1, D', E'_2) → poly3', e'_6, c'_3, d'_2
  30. Polygon(D'_1, E'_3, A'_1) → poly4', a'_3, d'_3, e'_7
  31. Polygon(A, B, C, D) → poly5, a, b, c, d
  32. Polygon(A, B, E) → poly6, e, a_1, b_1
  33. Polygon(B, C, E) → poly7, e_1, b_2, c_1
  34. Polygon(C, D, E) → poly8, e_2, c_2, d_1
  35. Polygon(A, D, E) → poly9, e_3, a_2, d_2