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圆的面积探索

圆的面积探索
几何画板及绘图内容加载中，请稍等……
2020-04-01 13:25
圆函数几何作图
这个范例演示了如何通过几何作图探索圆的面积。核心数学概念包括圆的性质和面积公式。通过使用GeoGebra命令如Intersect、Point、Segment、Circle等，可以动态地展示圆的面积变化。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. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(A, C) → f
  4. Circle(B, C) → c
  5. Sequence(Rotate[C, (n * θ), B], n, 1, a) → l1
  6. Segment(B, C) → g
  7. Sequence(Segment[Rotate[B, (n * θ), B], Rotate[C, (n * θ), B]], n, 1, a) → l2
  8. Sequence(Sector[c, ((n - 1) * θ), (n * θ)], n, 1, a) → l3
  9. Sequence(Sector[c, ((n - 1) * θ) + 180°, (n * θ) + 180°], n, 1, a) → l4
  10. Sequence((x(C) + 1 + (n * m), 0), n, 0, a) → l6
  11. Sequence((x(C) + 1 + (n * m) + m / 2, 0), n, 0, a - 1) → l5
  12. Sequence((x(C) + 1 + (n * m) + m / 2, (4 * cos(θ / 2))), n, 0, a - 1) → l7
  13. Sequence((x(C) + 1 + (n * m), (-4 * cos(θ / 2))), n, 1, a) → l9
  14. Sequence(Sector[Circle[(x(C) + 1 + ((n + 1) * m), (-4 * cos(θ / 2))), 4], (x(C) + 1 + ((n + 1) * m) + m / 2, 0), (x(C) + 1 + (n * m) + m / 2, 0)], n, 0, a - 1) → l15
  15. Vector((0, 0), (0, fit)) → u
  16. Translate(l15, u) → l15'
  17. Sequence(Sector[Circle[(x(C) + 1 + (n * m) + m / 2, 0), 4], (x(C) + 1 + (n * m), (-4 * cos(θ / 2))), (x(C) + 1 + ((n + 1) * m), (-4 * cos(θ / 2)))], n, 0, a - 1) → l8
  18. Segment((x(C) + 1, (-4 * cos(θ / 2))), (x(C) + 1 + (a * m), (-4 * cos(θ / 2)))) → h
  19. Segment((x(C) + 1 + m / 2, 0), (x(C) + 1 + m / 2, (-4 * cos(θ / 2)))) → i