积极 AI Logo 积极 AI

可调节面积模型

可调节面积模型
几何画板及绘图内容加载中，请稍等……
2018-08-24 01:51
多边形函数解析几何滑块动画函数图像
①本范例演示通过动态调整多边形边长和顶点位置来展示面积变化的现象；②涉及的核心数学概念包括多边形面积计算、乘法原理、二项式分布、相关性、自然数、条形图、多项式函数；③作图要点提炼自构造摘要，使用了Polygon（多边形）、Sequence（数列）、Point（点）、Text（文本）等GeoGebra命令和对象；④适合高中数学教学，用于直观理解函数、统计与几何的综合应用。

GeoGebra 命令及参数

  1. Polygon((0, 0), (factor1, 0), (factor1, factor2), (0, factor2)) → q1, f, g, h, i
  2. Sequence(Point[{i, factor2}], i, 0, factor1) → L_1
  3. Sequence(Point[{0, i}], i, 0, factor2) → L_2
  4. Point(L_1) → A
  5. Point(L_2) → B
  6. Polygon((0, 0), B, (x(A), y(B)), (x(A), 0)) → q2, j, b_1, k, l
  7. Polygon(B, (0, factor2), A, (x(A), y(B))) → q3, b_2, m, a_1, n
  8. Polygon((x(A), y(B)), A, (factor1, factor2), (factor1, y(B))) → q4, p, a_2, q, r
  9. Polygon((x(A), y(B)), (factor1, y(B)), (factor1, 0), (x(A), 0)) → q5, s, t, e, f_1
  10. Text(factor1 - x(A), Midpoint[a_2] + (0, height)) → factor1part2
  11. Text("+", A + (0, height)) → topPlus
  12. Text("+", B - (left, 0)) → leftPlus
  13. Text(y(B), Midpoint[j] - (left, 0)) → factor2part2
  14. Text(factor2 - y(B), Midpoint[b_2] - (left, 0)) → factor2part1
  15. Text(((factor2 - y(B)) * x(A)), Centroid[q3]) → area3
  16. Text((y(B) * x(A)), Centroid[q2]) → area2
  17. Text(((factor2 - y(B)) * (factor1 - x(A))), Centroid[q4]) → area4
  18. Text((y(B) * (factor1 - x(A))), Centroid[q5]) → area5
  19. Text((factor1 * factor2)) → text2
  20. Text(x(A), Midpoint[m] + (0, height)) → factor1part1
  21. Text("?", Midpoint[m] + (0, height)) → f1p1q
  22. Text("?", Midpoint[a_2] + (0, height)) → f1p2q
  23. Text("?", Midpoint[b_2] - (left, 0)) → f2p1q
  24. Text("?", Midpoint[j] - (left, 0)) → f2p2q