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Toboggan Trajectory and Geometric Construction

Toboggan Trajectory and Geometric Construction
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2018-05-20 00:30
FunctionTrigonometryCoordinate GeometryDerivativeGeometric Construction
This example demonstrates the generation and geometric analysis of a toboggan trajectory, involving core math concepts like intersections, boxplots, differences and slopes, straight lines, and equilateral triangles. It utilizes commands and objects such as CurveCartesian, Point, CircleArc, Surface, Sequence, and Derivative in GeoGebra for construction. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. CurveCartesian((3 * cos(t)), (3 * sin(t)), t, t, 0, 9.42477796076938) → a
  2. CurveCartesian(cos(t), sin(t), t, t, 0, 9.42477796076938) → b
  3. Point(xAxis) → C
  4. CircleArc(C, B, A) → c
  5. Surface(((-f(u)) * cos(v)) + (g(u) * sin(v)), ((-f(u)) * sin(v)) - (g(u) * cos(v)), k(u) + v, u, Umin, Umax, v, 0, Vmax) → e
  6. Sequence(CurveCartesian[((-f(u)) * cos((pk * Vmax))) + (g(u) * sin((pk * Vmax))), ((-f(u)) * sin((pk * Vmax))) - (g(u) * cos((pk * Vmax))), k(u) + (pk * Vmax), u, Umin, Umax], pk, 0, 1, 1 / n) → list1
  7. Derivative(fx) → fx'
  8. Derivative(fy) → fy'
  9. Derivative(fz) → fz'