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百分比：销售问题、利润与损失

百分比：销售问题、利润与损失
几何画板及绘图内容加载中，请稍等……
2020-08-26 10:37
多边形数列几何作图
这个范例演示了百分比在销售问题中的应用，重点展示利润与亏损的计算过程。核心数学概念包括百分比计算、利润率、亏损率以及基本的几何作图技巧。作图要点包括使用Point、Polygon、Intersection等命令创建图形，利用Sequence生成数据列表，应用If条件控制变化，计算成本与利润变化，并通过Midpoint和Segment绘制相关线段。适合初中生或高中数学学习，用于理解商业数学应用和几何作图方法。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Point(Segment[A, A + ((length * maxchange), 0)]) → P
  4. Point(Segment[A + (0, width), A + ((length * maxchange), width)]) → Q
  5. Polygon(A, P, P + (0, width), A + (0, width)) → poly1, poly1a, poly1d, poly1b, poly1c
  6. Polygon(B, B + (length, 0), B + (length, width), B + (0, width)) → poly2, poly2b, poly2a, poly2c, poly2d
  7. Intersect(Ray[P, P + (1, 0)], x = length) → A1
  8. Intersect(Ray[Q, Q + (1, 0)], x = length) → A2
  9. Intersect(Ray[B1, B1 + (1, 0)], x = x(P)) → P'
  10. Intersect(Ray[B2, B2 + (1, 0)], x = x(P)) → Q'
  11. Polygon(P, Q, A2, A1) → poly3, poly3b, poly3b_1, poly3d, poly3c
  12. Polygon(B1, B2, Q', P') → poly4, poly4c, poly4d, poly4b, poly4a
  13. Sequence(Segment[B + ((i * length / 10), 0), B + ((i * length / 10), width)], i, 1, 9) → list1
  14. Sequence(Sequence[Segment[B + ((j * length / 100) + (i * length / 10), 0), B + ((j * length / 100) + (i * length / 10), width)], j, 1, 9], i, 0, 9) → list2
  15. Sequence(Segment[A + ((i * length / 10), 0), A + ((i * length / 10), width)], i, 1, 9) → list3
  16. Sequence(Sequence[Segment[A + ((j * length / 100) + (i * length / 10), 0), A + ((j * length / 100) + (i * length / 10), width)], j, 1, 9], i, 0, 9) → list4
  17. Textfield(cost) → inputBox1
  18. Textfield(cost) → inputBox2
  19. Midpoint(B, B2) → C
  20. Midpoint(A, Q) → D
  21. Midpoint(P, A2) → E
  22. Midpoint(B1, Q') → F
  23. Midpoint(B1, Q') → G
  24. Textfield(price) → inputBox3
  25. Midpoint(P, A1) → H
  26. Midpoint(poly4a) → I
  27. Midpoint(poly3b_1) → J
  28. Midpoint(poly4d) → K
  29. If(o_2, "$ y", "$" + cost) → text9
  30. If(o_2, "$ y", "$" + cost) → text4
  31. If(o_3, "y %", (abs(change_%) * "%")) → text11
  32. If(o_1, "$ y", "$" + price) → text13
  33. If(change_% < 0, "-", "+") → text24
  34. If(o_3, "y %", (abs(change_%) * "%")) → text17
  35. If(o_3, (("1 " * text24) * " y %"), "1 " + ((((text24 * " ") * abs(change_%)) * "%"))) → text34
  36. If(o_3, (("1 " * text24) * " y %"), "1 " + ((((text24 * " ") * abs(change_%)) * "%"))) → text14
  37. If(o_1 ∨ o_4, If[o_1, "$ y", (((cost * " ") * text24) * " $ y")], "$" + price) → text12
  38. If(o_4, (((cost * " ") * text24) * " $ y"), "$" + price) → text15
  39. Textfield(price) → inputBox4
  40. Segment(B + (0, width), A) → g
  41. Segment(B2, A + (length, 0)) → i
  42. Segment(P, If[x(P) < length, Intersect[poly2c, x = x(P)], Intersect[poly4d, x = x(P)]]) → h
  43. Sequence(Segment[A + ((i * length / 10), 0), A + ((i * length / 10), width)], i, 1, floor((x(P) / length * 10))) → list3_1
  44. Sequence(Sequence[Segment[A + ((j * length / 100) + (i * length / 10), 0), A + ((j * length / 100) + (i * length / 10), width)], j, 1, 9], i, 0, floor((x(P) / length * 10)) - 1) → list4_1
  45. Sequence(Segment[B + ((i * length / 10), 0), B + ((i * length / 10), width)], i, 1, floor((x(P) / length * 10))) → list5
  46. Sequence(Sequence[Segment[B + ((j * length / 100) + (i * length / 10), 0), B + ((j * length / 100) + (i * length / 10), width)], j, 1, 9], i, 0, floor((x(P) / length * 10)) - 1) → list6_1
  47. Sequence(Segment[A + ((j * length / 100) + (floor((x(P) / length * 10)) * length / 10), 0), A + ((j * length / 100) + (floor((x(P) / length * 10)) * length / 10), width)], j, 1, floor(((x(P) - (floor((x(P) / length * 10)) * length / 10)) / length * 100))) → list4_2
  48. Sequence(Segment[B + ((j * length / 100) + (floor((x(P) / length * 10)) * length / 10), 0), B + ((j * length / 100) + (floor((x(P) / length * 10)) * length / 10), width)], j, 1, floor(((x(P) - (floor((x(P) / length * 10)) * length / 10)) / length * 100))) → list6_2
  49. If(b ∧ change_% < 0, "Loss", "Discount") → text8
  50. If(b, "Cost", "Marked Price") → text6

AI 绘图提示语参考

绘制一个矩形区域，分为两个部分，分别表示成本和售价。在成本部分，绘制一系列垂直线段表示成本变化，售价部分也绘制一系列垂直线段表示售价变化。在两个矩形之间绘制两条斜线，表示成本和售价的转换关系。在矩形内绘制一些辅助线段，表示成本和售价的变化区间。在矩形上添加文本框，输入成本和售价的具体数值。
以上提示语为根据原始绘图命令整理而来，仅供参考。