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动画演示梯形面积

动画演示梯形面积
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2017-06-26 18:39
多边形解析几何微积分
①本范例通过动画演示梯形面积的计算方法；②涉及核心数学概念包括梯形、相似三角形、方程、定积分、线性回归、条形图；③构造要点使用了Point, Sort, Element, DynamicCoordinates, Midpoint, If, Vector, Translate, Rotate, Semicircle, LaTeX, Polygon等GeoGebra命令和对象；④适合高中数学教学，用于帮助学生直观理解梯形面积公式及积分应用。

GeoGebra 命令及参数

  1. Point(xAxis) → H
  2. Point(xAxis) → I
  3. Sort({H, I}) → list1
  4. Element(list1, 1) → A
  5. Element(list1, 2) → B
  6. DynamicCoordinates(K, Min[Max[x(K), x(A)], x(B)], y(K)) → L
  7. Midpoint(L, I) → D
  8. If(animate > 0.5, (2 * animate) - 1, 0) → animate2
  9. DynamicCoordinates(P, Min[Max[x(P), x(A)], x(B)], y(L)) → T
  10. Midpoint(T, H) → E
  11. Vector(E, (x(H), y(E))) → b
  12. Translate(E, Vector[(b * animate2)]) → E'_1
  13. Rotate(L, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → L'
  14. Rotate(D, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → D'_1
  15. Rotate(T, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → T'
  16. Rotate(E, ((If[animate < 0.5, animate, 0.5] * 2) * π), D) → E'
  17. Translate(E', Vector[(b * animate2)]) → E''
  18. Semicircle(C, B) → d
  19. Point(d, 1 - animate) → G
  20. Vector(H - (0, 1), I - (0, 1)) → u
  21. Vector(I - (0, 1), H - (0, 1)) → v
  22. Vector(J, M) → w
  23. Vector(M, J) → j
  24. Vector(N, J) → k
  25. Vector(J, N) → l
  26. LaTeX("\frac{h}{2}") → text3
  27. DynamicCoordinates(P, Min[Max[x(K), x(A)], x(B)], y(K)) → Q
  28. Polygon(D, E, T, L) → poly1, p, q, r, s
  29. Rotate(D, (animate * π), D) → D'
  30. Polygon(I, H, E'_1, D) → poly2, h, i, m, n
  31. Rotate(L, (animate * π), D) → K'
  32. Polygon(D'_1, E'', T', L') → poly1', t, c, e, f_1
  33. LaTeX("Area = \frac{h}{2}(a+b)") → text4
  34. Vector(E) → a
  35. If(animate < 0.5, animate, 0.5) → animate1
  36. Midpoint(L', T') → S
  37. Midpoint(T', H) → F
  38. Vector(H - (0, 1), T' - (0, 1)) → f
  39. Vector(T' - (0, 1), H - (0, 1)) → g