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圆的面积演示 by Malin Christersson

圆的面积演示 by Malin Christersson
几何画板及绘图内容加载中，请稍等……
2014-02-18 22:47
圆向量几何作图
所属专题 CCSS G-GMD Geometric Measurement and Dimension Areas/Heights Areas/Heights Area and Circumference Explained
这个范例演示了如何通过几何作图计算圆的面积。核心数学概念包括圆的性质和几何作图。使用了Sequence, Point, OrthogonalLine, Mirror, Intersect, Vector等GeoGebra命令。适合初中及以上学生学习几何和面积计算。

GeoGebra 命令及参数

  1. Sequence((((2 * i) - 1) * a), i, 1, n) → angles
  2. Sequence(Vector[(d * Vector[(cos((-Element[angles, i])), sin((-Element[angles, i])))])], i, 1, n) → vectors
  3. Sequence(Midpoint[Cell[2, i], Cell[2, 1 + i]], i, 1, n) → midpoints
  4. Sequence(Intersect[Circle[Cell[2, i], 1], OrthogonalLine[Element[midpoints, i], Line[Cell[2, i], Cell[2, 1 + i]]]], i, 1, n) → lowpoints
  5. Sequence(Mirror[Element[lowpoints, i], yAxis], i, 1, n) → lowpoints2
  6. Sequence(Midpoint[Cell[3, i], Cell[3, 1 + i]], i, 1, n) → midpointsDown
  7. Sequence(Intersect[Circle[Cell[3, i], 1], OrthogonalLine[Element[midpointsDown, i], Line[Cell[3, i], Cell[3, 1 + i]]]], i, 1, n) → uppoints
  8. Sequence(Mirror[Element[uppoints, i], yAxis], i, 1, n) → uppoints2
  9. Point(yAxis) → B
  10. OrthogonalLine(B, yAxis) → g
  11. Point(g) → C
  12. Mirror(C, yAxis) → C'
  13. Point(h) → D
  14. Mirror(D, (-2, -0.5)) → D'
  15. Intersect(b, xAxis) → E
  16. Intersect(c, h) → F
  17. Intersect(e, g) → G
  18. Intersect(g, f) → H
  19. Vector(D', I) → u
  20. Vector(D, F) → v
  21. Vector(C', G) → w
  22. Vector(C, H) → z
  23. Sequence(CircleSector[Element[uppoints, i], Cell[3, 1 + i], Cell[3, i]], i, 1, n, 2) → sectorsDown1
  24. Sequence(CircleSector[Element[uppoints2, i], Mirror[Cell[3, i], yAxis], Mirror[Cell[3, 1 + i], yAxis]], i, 1, n, 2) → sectorsDown3
  25. Sequence(CircleSector[Element[lowpoints, i], Cell[2, 1 + i], Cell[2, i]], i, 1, n, 2) → sectors1
  26. Sequence(CircleSector[Element[lowpoints2, i] + ((2 * x(A)), 0), Mirror[Cell[2, i], yAxis] + ((2 * x(A)), 0), Mirror[Cell[2, 1 + i], yAxis] + ((2 * x(A)), 0)], i, 1, n, 2) → sectors3
  27. Sequence(CircleSector[Element[lowpoints, i], Cell[2, 1 + i], Cell[2, i]], i, 2, n, 2) → sectors2
  28. Sequence(CircleSector[Element[lowpoints2, i] + ((2 * x(A)), 0), Mirror[Cell[2, i], yAxis] + ((2 * x(A)), 0), Mirror[Cell[2, 1 + i], yAxis] + ((2 * x(A)), 0)], i, 2, n, 2) → sectors4
  29. Sequence(CircleSector[Element[uppoints, i], Cell[3, 1 + i], Cell[3, i]], i, 2, n, 2) → sectorsDown2
  30. Sequence(CircleSector[Element[uppoints2, i], Mirror[Cell[3, i], yAxis], Mirror[Cell[3, 1 + i], yAxis]], i, 2, n, 2) → sectorsDown4

AI 绘图提示语参考

画一个圆形，通过几何构造展示其面积计算方法。首先绘制多个向量从圆心出发，然后在这些向量与圆相交处找到点，并将这些点沿 y 轴对称反射，形成上下两排点。接着连接上下两排点，形成多个扇形，这些扇形组合起来近似一个圆形，从而直观展示圆形面积的计算原理。
以上提示语为根据原始绘图命令整理而来，仅供参考。