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分享果汁的杯子

分享果汁的杯子
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2018-11-29 00:54
向量函数几何作图
①这个范例演示了如何通过GeoGebra动态展示果汁在多个杯子间分配的过程，涉及图形变换与数量关系；②核心数学概念包括除法、单位圆、二次函数、三维向量、多项式函数、对称性；③作图要点使用了Polygon（多边形）、CountIf（计数条件）、If（条件判断）等命令，创建了多个杯子对象（A_3到D_2）和轨迹线（L系列）；④适合高中数学教学，用于可视化理解函数、向量及几何变换。

GeoGebra 命令及参数

  1. Polygon(A_3, B_3, C_3, D_3) → q3, a_2, b_2, c_9, d_2
  2. Polygon(A_2, B_2, C_2, D_2) → q2, a_1, b_1, c_8, d_1
  3. CountIf(IsInRegion[T, q2], T, {L_{v1}, L_{v2}, L_{v3}, L_{v4}, L_{v5}, L_{v6}, L_{v7}}) → vazios_{t2}
  4. CountIf(IsInRegion[T, q3], T, {L_{v1}, L_{v2}, L_{v3}, L_{v4}, L_{v5}, L_{v6}, L_{v7}}) → vazios_{t3}
  5. CountIf(IsInRegion[T, q3], T, {L_{c1}, L_{c2}, L_{c3}, L_{c4}, L_{c5}, L_{c6}, L_{c7}}) → cheios_{t3}
  6. CountIf(IsInRegion[T, q2], T, {L_{c1}, L_{c2}, L_{c3}, L_{c4}, L_{c5}, L_{c6}, L_{c7}}) → cheios_{t2}
  7. CountIf(IsInRegion[T, q3], T, {L_{m1}, L_{m2}, L_{m3}, L_{m4}, L_{m5}, L_{m6}, L_{m7}}) → meios_{t3}
  8. CountIf(IsInRegion[T, q2], T, {L_{m1}, L_{m2}, L_{m3}, L_{m4}, L_{m5}, L_{m6}, L_{m7}}) → meios_{t2}
  9. Polygon(A_1, B_1, C_1, D_1) → q1, a, b, c, d
  10. CountIf(IsInRegion[T, q1], T, {L_{c1}, L_{c2}, L_{c3}, L_{c4}, L_{c5}, L_{c6}, L_{c7}}) → cheios_{t1}
  11. CountIf(IsInRegion[T, q1], T, {L_{m1}, L_{m2}, L_{m3}, L_{m4}, L_{m5}, L_{m6}, L_{m7}}) → meios_{t1}
  12. CountIf(IsInRegion[T, q1], T, {L_{v1}, L_{v2}, L_{v3}, L_{v4}, L_{v5}, L_{v6}, L_{v7}}) → vazios_{t1}
  13. If(cheios_{t1} ≟ 3 ∧ meios_{t1} ≟ 1 ∧ vazios_{t1} ≟ 3 ∧ cheios_{t2} ≟ 3 ∧ meios_{t2} ≟ 1 ∧ vazios_{t2} ≟ 3 ∧ cheios_{t3} ≟ 1 ∧ meios_{t3} ≟ 5 ∧ vazios_{t3} ≟ 1, 1, 0) → s_1
  14. If(IsInRegion[L_{c1}, q1], s_1 ≟ 1) → e
  15. If(cheios_{t1} ≟ 1 ∧ meios_{t1} ≟ 5 ∧ vazios_{t1} ≟ 1 ∧ cheios_{t2} ≟ 3 ∧ meios_{t2} ≟ 1 ∧ vazios_{t2} ≟ 3 ∧ cheios_{t3} ≟ 3 ∧ meios_{t3} ≟ 1 ∧ vazios_{t3} ≟ 3, 1, 0) → s_2
  16. If(cheios_{t1} ≟ 3 ∧ meios_{t1} ≟ 1 ∧ vazios_{t1} ≟ 3 ∧ cheios_{t2} ≟ 1 ∧ meios_{t2} ≟ 5 ∧ vazios_{t2} ≟ 1 ∧ cheios_{t3} ≟ 3 ∧ meios_{t3} ≟ 1 ∧ vazios_{t3} ≟ 3, 1, 0) → s_3
  17. If(cheios_{t1} ≟ 3 ∧ meios_{t1} ≟ 1 ∧ vazios_{t1} ≟ 3 ∧ cheios_{t2} ≟ 2 ∧ meios_{t2} ≟ 3 ∧ vazios_{t2} ≟ 2 ∧ cheios_{t3} ≟ 2 ∧ meios_{t3} ≟ 3 ∧ vazios_{t3} ≟ 2, 1, 0) → s_4
  18. If(cheios_{t1} ≟ 2 ∧ meios_{t1} ≟ 3 ∧ vazios_{t1} ≟ 2 ∧ cheios_{t2} ≟ 3 ∧ meios_{t2} ≟ 1 ∧ vazios_{t2} ≟ 3 ∧ cheios_{t3} ≟ 2 ∧ meios_{t3} ≟ 3 ∧ vazios_{t3} ≟ 2, 1, 0) → s_5
  19. If(cheios_{t1} ≟ 2 ∧ meios_{t1} ≟ 3 ∧ vazios_{t1} ≟ 2 ∧ cheios_{t2} ≟ 2 ∧ meios_{t2} ≟ 3 ∧ vazios_{t2} ≟ 2 ∧ cheios_{t3} ≟ 3 ∧ meios_{t3} ≟ 1 ∧ vazios_{t3} ≟ 3, 1, 0) → s_6

AI 绘图提示语参考

绘制一个动态果汁分配的几何图形，展示多个杯子中的果汁分布。使用多边形表示杯子，通过计数和条件判断显示果汁（红色）、半满（蓝色）和空（绿色）的状态。图形包含三个层级的杯子，每个层级有不同数量的果汁状态。通过线条连接表示果汁流动路径，整体构造体现几何变换和对称性，适合教学演示函数、向量和几何关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。