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实数缠绕在单位圆上

实数缠绕在单位圆上
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2019-09-09 07:35
圆角函数
这个范例展示了如何将实数缠绕在单位圆上。核心数学概念包括实数、单位圆和角度。通过使用If语句、点、文本框和角度等GeoGebra命令，可以构造出实数与单位圆之间的对应关系。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. If(X_1 ≥ 0, Arc[c, (1, 0), (cos(X_1), sin(X_1))], Arc[c, (cos(X_1), sin(X_1)), (1, 0)]) → X
  2. If(X_1 > 0, If[((-1)^(floor(X_1 / π)) * x) < ((-1)^(floor(X_1 / π)) * cos(X_1)), (((-cos(X_1))) / sin(X_1) * (x - cos(X_1))) + sin(X_1)]) → f
  3. If(X_1 ≟ 0, x = 1) → g
  4. If(X_1 > 0, Segment[(1, 0), (1, -10)], X_1 < 0, Segment[(1, 0), (1, 10)]) → h
  5. If(X_1 < 0, If[((-1)^(floor(X_1 / π)) * x) > ((-1)^(floor(X_1 / π)) * cos(X_1)), (((-cos(X_1))) / sin(X_1) * (x - cos(X_1))) + sin(X_1)]) → p
  6. If(0 < X_1 < 1, Point[{cos(X_1) - ((1 - X_1) * sin(X_1)), sin(X_1) + ((1 - X_1) * cos(X_1))}]) → B
  7. If(X_1 ≥ 1, Point[{cos(1), sin(1)}]) → C
  8. If(0 < X_1 < 2, Point[{cos(X_1) - ((2 - X_1) * sin(X_1)), sin(X_1) + ((2 - X_1) * cos(X_1))}]) → D
  9. If(X_1 ≤ 0, Point[{1, 2}]) → E
  10. If(X_1 ≤ 0, Point[{1, 1}]) → A
  11. If(X_1 ≥ 2, Point[{cos(2), sin(2)}]) → F
  12. If(X_1 ≤ 0, Point[{1, 3}]) → G
  13. If(0 < X_1 < 3, Point[{cos(X_1) - ((3 - X_1) * sin(X_1)), sin(X_1) + ((3 - X_1) * cos(X_1))}]) → H
  14. If(X_1 ≥ 3, Point[{cos(3), sin(3)}]) → I
  15. If(X_1 ≥ 0, Point[{1, -1}]) → J
  16. If(-1 < X_1 < 0, Point[{cos(X_1) - ((-1 - X_1) * sin(X_1)), sin(X_1) + ((-1 - X_1) * cos(X_1))}]) → K
  17. If(X_1 ≤ -1, Point[{cos(-1), sin(-1)}]) → L
  18. If(X_1 ≥ 0, Point[{1, -2}]) → M
  19. If(-2 < X_1 < 0, Point[{cos(X_1) - ((-2 - X_1) * sin(X_1)), sin(X_1) + ((-2 - X_1) * cos(X_1))}]) → N
  20. If(X_1 ≤ -2, Point[{cos(-2), sin(-2)}]) → O
  21. If(X_1 ≥ 0, Point[{1, -3}]) → P
  22. If(-3 < X_1 < 0, Point[{cos(X_1) - ((-3 - X_1) * sin(X_1)), sin(X_1) + ((-3 - X_1) * cos(X_1))}]) → Q
  23. If(X_1 ≤ -3, Point[{cos(-3), sin(-3)}]) → R
  24. If(X_1 ≥ 0, Point[{1, -4}]) → S
  25. If(-4 < X_1 < 0, Point[{cos(X_1) - ((-4 - X_1) * sin(X_1)), sin(X_1) + ((-4 - X_1) * cos(X_1))}]) → T
  26. If(X_1 ≤ -4, Point[{cos(-4), sin(-4)}]) → U
  27. If(0 < X_1 < 4, Point[{cos(X_1) - ((4 - X_1) * sin(X_1)), sin(X_1) + ((4 - X_1) * cos(X_1))}]) → W
  28. If(X_1 ≥ 4, Point[{cos(4), sin(4)}]) → Z
  29. Point({cos(X_1), sin(X_1)}) → A_1
  30. If(X_1 ≤ 0, Point[{1, 4}]) → V
  31. If(X_1 ≤ 0, Point[{1, 5}]) → B_1
  32. If(0 < X_1 < 5, Point[{cos(X_1) - ((5 - X_1) * sin(X_1)), sin(X_1) + ((5 - X_1) * cos(X_1))}]) → C_1
  33. If(X_1 ≥ 5, Point[{cos(5), sin(5)}]) → D_1
  34. If(X_1 ≤ 0, Point[{1, 6}]) → E_1
  35. If(0 < X_1 < 6, Point[{cos(X_1) - ((6 - X_1) * sin(X_1)), sin(X_1) + ((6 - X_1) * cos(X_1))}]) → F_1
  36. If(X_1 ≥ 6, Point[{cos(6), sin(6)}]) → G_1
  37. Point({1, 0}) → H_1
  38. Textfield(X_1) → InputBox1
  39. Point({cos(X_1), sin(X_1)}) → myPoint
  40. Angle(Vector[(1, 0)], victor) → θ
  41. Angle(victor, Vector[(1, 0)]) → theta