积极 AI Logo 积极 AI

圆的周长探索

圆的周长探索
几何画板及绘图内容加载中，请稍等……
2015-12-08 08:40
圆解析几何几何作图
本范例通过测量不同圆的直径和周长，探索圆的周长与直径之间的关系。核心数学概念包括圆的周长公式和比例关系。使用了Point, CurveCartesian, If, Segment, CircleArc, Sequence, Circle等GeoGebra命令。适合初中及以上学生学习圆的基本性质。

GeoGebra 命令及参数

  1. Point(yAxis) → B
  2. CurveCartesian((r * (t - sin(t))), (r * (1 - cos(t))) + y(B), t, 0, 6.28319) → f
  3. Point(f) → P
  4. If(x(P) < (r * 3.141592653589793), acos(1 - (y(P) - y(B)) / r), (2 * 3.141592653589793) - acos(1 - (y(P) - y(B)) / r)) → θ
  5. Point(Segment[(x(D0), y(D0) + 0.25), ((r * θ) - r, r + y(B))]) → A
  6. Segment(B, (x(C_1), y(B))) → c1
  7. CircleArc(C_1, (x(C_1), y(B)), P) → c2
  8. CircleArc(C_1, P, (x(C_1), y(B))) → e
  9. Segment(A, (x(A) + (2 * r), y(A))) → j
  10. Sequence(Segment[(((2 * i) * r), 0), (((2 * i) * r), -0.25)], i, 0, 10) → list1
  11. Sequence(Segment[((((2 * i) - 1) * r), 0), ((((2 * i) - 1) * r), -0.2)], i, 1, 10) → list2
  12. Sequence(Sequence[Segment[((i * r) + ((0.2 * j) * r), 0), ((i * r) + ((0.2 * j) * r), -0.15)], j, 1, 4], i, 0, 19) → list3
  13. Segment(B, (x(B) + (20 * r), y(B))) → c
  14. Sequence(Segment[(i, 0), (i, -0.25)], i, 0, 10) → list6
  15. Sequence(Segment[(((2 * i) - 1) / 2, 0), (((2 * i) - 1) / 2, -0.2)], i, 1, 10) → list7
  16. Sequence(Sequence[Segment[(i / 2 + (0.1 * j), 0), (i / 2 + (0.1 * j), -0.15)], j, 1, 4], i, 0, 19) → list8
  17. Sequence(Segment[(((2 * i) - 1) / 20, 0), (((2 * i) - 1) / 20, -0.1)], i, 1, 100) → list10
  18. Sequence(Segment[((((2 * i) - 1) * r / 10), 0), ((((2 * i) - 1) * r / 10), -0.1)], i, 1, 100) → list4
  19. Segment((0, 0), (10, 0)) → a
  20. Sequence(Segment[(((2 * i) - 1) / 200, 0), (((2 * i) - 1) / 200, -0.03)], i, 1, 1000) → list11
  21. Sequence(Sequence[Segment[(i / 20 + (0.01 * j), 0), (i / 20 + (0.01 * j), -0.06)], j, 1, 4], i, 0, 199) → list9
  22. Sequence(Sequence[Segment[((i * r / 10) + ((0.02 * j) * r), 0), ((i * r / 10) + ((0.02 * j) * r), -0.06)], j, 1, 4], i, 0, 199) → list5
  23. Circle((0, r), r) → d
  24. Corner(1) → cor1
  25. Corner(2) → cor2
  26. Corner(3) → cor3
  27. Corner(4) → cor4