积极 AI Logo 积极 AI

看见乘法

看见乘法
几何画板及绘图内容加载中，请稍等……
2016-09-02 00:49
解析几何最值优化
所属专题 Elementary School Applets Multiplication and Division - Visuals Multiplication and Division - Visuals Multiplication and Division - Visuals
①本范例通过动态图形演示乘法的几何意义，将抽象的乘法运算转化为直观的图形叠加与面积计算；②涉及的核心数学概念包括乘法、线性规划、同余、加法、概率和百分比；③作图要点运用了Textfield, If, Sequence, Segment, Max, First, CurveCartesian等GeoGebra命令与对象，如通过滑块动态调整参数并实时显示结果；④适合初中及以上学生使用，可用于理解乘法运算的几何本质及线性规划初步概念。

GeoGebra 命令及参数

  1. Textfield(a1text) → InputBox2
  2. Textfield(a2text) → InputBox1
  3. If(a1 < 5, 1, If[a1 < 9, 2, 3]) → groupLayoutSizes
  4. Sequence(Element[Flatten[Sequence[Sequence[Point[{(4.5 / groupLayoutSizes * i), (9 / groupLayoutSizes * j)}], i, 0, a1 - 1], j, 0, groupLayoutSizes - 1]], k], k, 1, (a1 * groupLayoutSizes), groupLayoutSizes) → groupCenters
  5. Sequence(Point[{i, 0}], i, 0, ((2 * a1) * a2), a2) → lineDots
  6. Segment(Element[lineDots, 1], (2 * Element[lineDots, Length[lineDots]])) → line
  7. Sequence(Point[{i, 0}], i, 0, line) → linemarks
  8. Max(a1, a2) → arraySize
  9. If(b, a1 + ((0.5 * arraySize) * sqrt(a2 / a1)), If[a, ((1.5 * a1) * a2), If[c, (5 * a1 / groupLayoutSizes), 10]]) → right
  10. If(b, ((-0.05 * arraySize) * sqrt(a1 / a2)), If[a, (-0.5 * a2 / π), If[c, -2, 0]]) → bottom
  11. Sequence(Sequence[Polygon[(i, j), (i + 1, j), 4], i, 0, a1 - 1], j, 0, a2 - 1) → array
  12. First(Element[array, 1], arrayTimer1) → firstArray
  13. First(array, arrayTimer2) → secondArray
  14. CurveCartesian((a2 / ((2 * π)) * (t - sin(t))), (a2 / ((2 * π)) * (1 - cos(t))), t, 0, jumpTimer) → d
  15. If(b, ((-0.5 * arraySize) * sqrt(a2 / a1)), If[a, ((-0.1 * a1) * a2), If[c, (-a1), -10]]) → left
  16. If(b, a2 + ((0.05 * arraySize) * sqrt(a1 / a2)), If[a, (1.5 * a2 / π), If[c, (groupLayoutSizes * 3), 10]]) → top
  17. First(Sequence[Circle[Element[groupCenters, i], 1.25], i, 1, Length[groupCenters]], circleTimer) → groupCircles
  18. First(Flatten[Sequence[Sequence[Element[groupCenters, i] + ((1 - a2) / a2 * (cos(((2 * π / a2) * j)), sin(((2 * π / a2) * j)))), j, 0, a2 - 1], i, 1, Length[groupCenters]]], dotTimer) → groupDots
  19. Sequence(Text[x(Element[lineDots, i]), Element[lineDots, i] + (((-right)) / 100, bottom / 2.5)], i, 1, Length[lineDots]) → lineText