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Rolling on the Inside

Rolling on the Inside
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2015-11-15 04:10
VectorCoordinate GeometryParametric EquationGeometric Construction
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates the locus of a point rolling inside a circle, involving vector operations, transformations, parametric equations, and coordinate geometry. Key GeoGebra commands used include Vector, CurveCartesian, Rotate, Translate, Point, and Circle, as outlined in the construction summary. Suitable for high school and advanced learners exploring spatial geometry and locus problems.

GeoGebra Commands & Parameters

  1. Vector(A) → u
  2. CurveCartesian((((n - 2) * cos(t)) + cos((t * (n - 2)))) / (n + 1), (((n - 2) * sin(t)) - sin((t * (n - 2)))) / (1 + n), t, 0, 6.28319) → a
  3. Rotate(a, ((-α)) / (n - 1), O) → a'
  4. Translate(a', u) → a''
  5. Point(xAxis) → B
  6. CurveCartesian((((n + 1) * cos(t)) - cos((t * (n + 1)))) / (n + 1) + x(B), (((n + 1) * sin(t)) - sin((t * (n + 1)))) / (n + 1) + y(B), t, 0, 6.28319) → b'
  7. CurveCartesian((((n - 1) * cos(t)) + cos((t * (n - 1)))) / (n + 1), (((n - 1) * sin(t)) - sin((t * (n - 1)))) / (n + 1), t, 0, 6.28319) → b
  8. CurveCartesian(((n * cos(t)) - cos((t * n))) / (n + 1) + x(B), ((n * sin(t)) - sin((t * n))) / (n + 1) + y(B), t, 0, 6.28319) → c
  9. Rotate(c, ((-α)) / (n - 1), B) → c'
  10. Translate(c', u) → c''
  11. Circle(O, A) → d
  12. Circle(B, A') → e