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平行四边形面积探索 by leucotea

平行四边形面积探索 by leucotea
几何画板及绘图内容加载中，请稍等……
2020-02-06 15:59
多边形向量数列解析几何几何作图
这个GeoGebra范例演示了不同形状的平行四边形面积，包括倾斜的平行四边形。核心数学概念包括几何作图和面积计算。通过使用Point, Ray, Translate, If, Intersect, Segment, Slope, Sequence, Rotate, Vector, Midpoint, Angle等命令，可以动态探索平行四边形的性质。适合初中及以上学生学习几何和面积计算。

GeoGebra 命令及参数

  1. Point(xAxis) → I
  2. Point(Ray[(x(I), 0), (x(I), 1)]) → J
  3. Ray((-0.01, y(J)), (-1, y(J))) → k
  4. Point(xAxis) → C
  5. Point(k) → A
  6. Translate(A, Vector[C]) → D
  7. If(floor(abs(x(D)) / base) ≟ abs(x(D)) / base, false, true) → more
  8. If(more, n + 1, n) → n'
  9. Intersect(xAxis, yAxis) → B
  10. Segment(A, B) → a
  11. Segment(B, C) → b
  12. Segment(C, D) → c
  13. Segment(D, A) → d
  14. Slope(a) → m
  15. Sequence(((i + 1) * x(C), m * x(C) * i), i, 0, n) → list1
  16. Point(Ray[(0, 0), (1, 0)]) → E
  17. Segment(E, F) → e
  18. Segment(F, G) → f
  19. Segment(G, H) → g
  20. Segment(H, E) → h
  21. Sequence((i * x(C), m * x(C) * i), i, 0, n) → list2
  22. Sequence(Polygon[Element[list2, i], Element[list1, i], Element[list2, i + 1]], i, 1, n) → list3
  23. Sequence(If[t < i, 0, If[t < i + 1, t - i, 1]], i, 0, n' - 1) → list_t
  24. Sequence(Polygon[Element[list1, i], Element[list2, i + 1], Element[list1, i + 1]], i, 1, n) → list4
  25. Sequence(Translate[Element[list3, i], Vector[(0, 0), (2 * Min[Element[list_t, i], 0.5] * (x(E) - (i - 1) * x(C)), 0)]], i, 1, n) → list5
  26. Sequence(Translate[Translate[Element[list4, i], Vector[(0, 0), (2 * Min[Element[list_t, i], 0.5] * (x(E) - (i - 1) * x(C)), 0)]], Vector[(0, 0), (2 * Max[Element[list_t, i] - 0.5, 0] * base, 0)]], i, 1, n) → list6
  27. If(more, Polygon[A, (n' * x(C), y(A)), Element[list1, n'], Element[list2, n']]) → last1
  28. If(more, Polygon[D, (n' * x(C), y(A)), Element[list1, n']]) → last2
  29. If(more, Translate[last1, Vector[(2 * Min[Element[list_t, n'], 0.5] * (n * base + x(E)), 0)]]) → last1'
  30. If(more, Translate[Translate[last2, Vector[(2 * Min[Element[list_t, n'], 0.5] * (n * base + x(E)), 0)]], Vector[(2 * Max[Element[list_t, n'] - 0.5, 0] * base, 0)]]) → last2'
  31. Segment(J, A) → i
  32. Segment(I, B) → j
  33. Rotate(J, 90*°, I) → J'
  34. Vector(I, J) → u
  35. Vector(J, I) → v
  36. Midpoint(I, J) → K
  37. Midpoint(b) → L
  38. Angle(J, I, Translate[I, Vector[If[x(I) > x(C), Vector[C], Vector[-C]]]]) → α
  39. Sequence(Segment[(0 + i, ymax), (0 + i, ymin)], i, 0, ceil(xmax)) → list7_1
  40. Sequence(Segment[(-i, ymax), (0 - i, ymin)], i, 1, ceil(abs(xmin))) → list7_2
  41. Sequence(Segment[(xmin, -i), (xmax, -i)], i, 1, ceil(abs(ymin))) → list8_2
  42. Sequence(Segment[(xmin, i), (xmax, i)], i, 0, ceil(ymax)) → list8_1
  43. Segment(I, J) → r