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Syntractrice Curve Demonstration

Syntractrice Curve Demonstration
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2015-12-22 21:44
FunctionTrigonometryCoordinate GeometryParametric Equation
In collections surface 3D surface 3D
This example demonstrates the properties and construction process of the syntractrice curve, a complex mathematical figure. It involves core concepts like coordinate geometry, piecewise functions, symmetry, and transformations. The construction utilizes GeoGebra commands and objects such as CurveCartesian, Segment, Point, If, Surface, Sequence, and Dilate. Suitable for high school and above, it helps learners understand the intricacies of constructing and analyzing complex curves.

GeoGebra Commands & Parameters

  1. CurveCartesian((a * (t - (k * tanh(t)))), (a * k / cosh(t)), t, (-f), f) → b
  2. Segment((-A), A) → p
  3. Point(p) → P
  4. Point(b, PathParameter[P]) → Mp
  5. If(d + 0.2 > f, f, d + 0.2) → ma
  6. If(d - 0.2 < (-f), (-f), d - 0.2) → mi
  7. Point(b) → M
  8. Point(p, PathParameter[M]) → Pm
  9. CurveCartesian((a * (t - (k * tanh(t)))), (a * k / cosh(t)), t, mi, ma) → e
  10. Point(e) → MM
  11. Surface((a * (u - (v * tanh(u)))), v, (a * v / cosh(u)), u, (-f), fm, v, 0, k) → g
  12. Segment((x(P), 0, y(P)), (x(M), k, y(M))) → h
  13. Segment((x(P), k, y(P)), (x(M), k, y(M))) → j
  14. Segment(P, M) → c
  15. Sequence(CurveCartesian[(a * (t - (i * tanh(t)))), (a * i / cosh(t)), t, (-f), f], i, 0, 12, 1) → liste2
  16. Segment((x(P), 0), (x(P), k)) → i
  17. Sequence(CurveCartesian[(a * (t - (i * tanh(t)))), i, (a * i / cosh(t)), t, (-f), f], i, 0, k, 1) → liste3
  18. Segment((x(P), 0), (x(P), 12)) → l
  19. Dilate(M_2, 12 / k, P_2) → M_3
  20. Segment((x(P), 12, 0), M_3) → m
  21. Sequence(Dilate[M_3, i, P_2], i, 0, 1, 1 / 12) → liste4
  22. Segment(P_2, M_3) → n
  23. Dilate(M, 12 / k, P) → M_1
  24. Sequence(Dilate[M_1, i, P], i, 0, 1, 1 / 12) → liste1