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Roll Out Arc - R = 1

Roll Out Arc - R = 1
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2016-10-19 06:00
CircleTrigonometryGeometric ConstructionLocus
This example demonstrates the path traced by a point on the circumference of a circle with radius 1 as it rolls along a straight line, forming a circle. Core mathematical concepts include the unit circle, equilateral triangles, rotation, parallelograms, frequency distribution, and scatter plots. Construction highlights the use of GeoGebra commands and objects like Rotate, Angle, CircleArc, Segment, and FractionText. Suitable for high school students learning about coordinate geometry and locus problems.

GeoGebra Commands & Parameters

  1. Rotate(R, α, O) → R'
  2. Angle(R, O, R') → β
  3. CircleArc(O, R, R') → c
  4. CircleArc(O, R', R) → d
  5. Segment(R, Tx) → a
  6. CircleArc(On, Tx, Rn) → e
  7. Rotate(Rn, 360° - α, On) → Rn'
  8. Angle(Rn, On, Rn') → γ
  9. CircleArc(On, Rn, Rn') → f
  10. Segment(On, Rn) → b
  11. Segment(On, Tx) → g
  12. Segment(On, Rn') → h
  13. FractionText(Q) → text3
  14. FractionText(x(Tx)) → text4