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Fibonacci Spiral & Number Line

Fibonacci Spiral & Number Line
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2019-09-17 18:22
FunctionTrigonometrySequenceCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationship between the Fibonacci spiral and the number line. It involves core mathematical concepts such as the Fibonacci sequence, golden ratio, analytical geometry, and trigonometric functions. Construction highlights include using GeoGebra commands like Point, Distance, Vector, Line, Angle, Segment, Intersect, Circle, CurveCartesian, and Semicircle. Suitable for high school students and enthusiasts to understand the connection between sequences and geometric shapes.

GeoGebra Commands & Parameters

  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