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斐波那契螺旋与数线

斐波那契螺旋与数线
几何画板及绘图内容加载中，请稍等……
2019-09-17 18:22
函数三角函数数列解析几何几何作图
①本范例演示斐波那契螺旋与数线的几何关系；②涉及核心数学概念包括斐波那契数列、黄金分割、解析几何、三角函数等；③作图要点：使用Point, Distance, Vector, Line, Angle, Segment, Intersect, Circle, CurveCartesian, Semicircle等GeoGebra命令构建图形；④适合高中及以上数学学习者和爱好者用于理解数列与几何图形的关联。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Distance(O, D) → distanceOD
  3. Vector(A, D) → vecAD
  4. Line(O, D) → line_{OD}
  5. Line(O, G) → line_{OC}
  6. Angle(G, O, D) → angle_{01}
  7. Segment(A, G) → segAG
  8. Segment(A, D) → segAD
  9. Intersect(line_{y1}, segAD) → E
  10. Intersect(line_{y1}, segAG) → F
  11. Line(G, D) → line_{GD}
  12. Intersect(line_{GD}, xAxis) → C
  13. Circle(O, D) → circle_{01}
  14. Intersect(circle_{01}, xAxis) → H, I
  15. Intersect(f_{r2-c}, xAxis, (0, 0)) → J
  16. CurveCartesian((((var_{r1} + radius) * t) * f_{r1-c}(t + spin + 0)) + tick_{L}, (((var_{r1} + radius) * t) * f_{r1-s}(t + spin + 0)) + 0, t, sV, eV) → curve_{01}
  17. CurveCartesian((((var_{r2} + radius) * t) * f_{r2-c}(t + spin + 0)) + tick_{L}, (((var_{r2} + radius) * t) * f_{r2-s}(t + spin + 0)) + 0, t, sV, eV) → curve_{02}
  18. Semicircle(B, A) → simicircle_{01}
  19. Semicircle(C, B) → simicircle_{02}
  20. Semicircle(A, C) → simicircle_{03}
  21. Vector(A, G) → vecAG