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恒定周长...变化的面积?

恒定周长...变化的面积?
几何画板及绘图内容加载中，请稍等……
2016-07-08 11:52
多边形最值优化几何作图
①本范例演示多边形在恒定周长下面积的变化规律；②涉及核心数学概念：周长、面积、多边形、优化问题；③作图要点：使用 GeoGebra 命令 Polygon, Area, Circle, Point, Segment, OrthogonalLine, Intersect, Perimeter, Distance, If 等构建图形并计算；④适合高中数学教学，用于理解周长固定时图形面积的最大化问题。

GeoGebra 命令及参数

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Area(poly1) → areaT
  3. Circle(D, perim / 2) → d
  4. Point(d) → E
  5. Segment(D, E) → e
  6. Point(e) → F
  7. OrthogonalLine(F, e) → f_1
  8. OrthogonalLine(D, e) → g
  9. Circle(F, E) → h
  10. Intersect(h, f_1, 2) → G
  11. OrthogonalLine(G, f_1) → i
  12. Intersect(g, i) → H
  13. Polygon(D, F, G, H) → poly2, d_1, f, g_1, f_2
  14. Perimeter(poly2) → k
  15. Circle(D, perim / 3) → p
  16. Intersect(p, d_1, 1) → I
  17. Segment(D, I) → a_1
  18. Segment(I, F) → b_1
  19. Segment(F, G) → b_2
  20. Segment(D, F) → l
  21. Intersect(r, xAxis, 2) → K
  22. Distance(I, K) → n
  23. Circle(F, a - l) → s
  24. OrthogonalLine(F, xAxis) → t
  25. Intersect(s, t) → L, M
  26. Segment(F, M) → e_1
  27. Segment(H_2, D) → c_2
  28. If(poly2 > poly1, 1, 0) → q
  29. Segment(H_2, H) → c_1
  30. Segment(M, G) → h_1
  31. Circle(H, c - c_2) → k_1
  32. Intersect(k_1, i) → J, N
  33. Segment(H, J) → i_1
  34. Segment(J, G) → j_1