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A Rolling Parabola

A Rolling Parabola
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2016-01-22 13:44
FunctionGeometric Construction
This example demonstrates the geometric shape formed by the locus of a rolling parabola. It involves core math concepts like parabola, polynomial functions, functions, isosceles triangles, power functions, and plane figures. Construction highlights include commands like If, Tangent, Intersect, Angle, Rotate, Translate, and objects such as t, a, f, xpos, A, s, b, B, α, A', L, C, D, loc1, c, E. Suitable for high school and above, exploring dynamic transformations and trajectory generation in functions.

GeoGebra Commands & Parameters

  1. If(x(A) ≥ 0, -1, 1) → s
  2. Tangent(A, f) → b
  3. Intersect(b, xAxis) → B
  4. Angle(b, xAxis) → α
  5. Rotate(A, (s * α), B) → A'
  6. If(t ≟ 0, 0, Length[f, 0, x(A)]) → L
  7. Translate(Rotate[(0, 1 / ((4 * a))), (s * α), B], C - A') → D
  8. Translate(Rotate[f, (s * α), B], C - A') → c