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Circumference of a Unit Circle

Circumference of a Unit Circle
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2017-08-30 18:33
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically prove that the circumference of a unit circle is 2π using GeoGebra. It involves core mathematical concepts such as the circumference formula of a circle, coordinate points in analytical geometry, rotation, and circle arc construction. Key GeoGebra commands/objects used include Intersect, Point, Ray, Circle, Rotate, CircleArc, and Segment. Suitable for high school students learning and understanding the basic properties of circles and parametric equations.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Point(yAxis) → B
  3. Ray(A, B) → a
  4. Point(a) → C
  5. Circle(O, r) → c
  6. Intersect(c, xAxis) → P,
  7. Rotate(P, (-t), O) → P'
  8. CircleArc(O, P, P') → d
  9. Point(Circle[A, s]) → D
  10. Segment(A, D) → b
  11. Circle(C, A) → e