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Circle Area - Inscribed/Circumscribed Polygons

Circle Area - Inscribed/Circumscribed Polygons
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2016-03-24 11:22
CirclePolygonTrigonometryLimitGeometric Construction
In collections Geometry - Area & Volume
This example demonstrates how the area of a circle can be approximated by inscribed and circumscribed polygons. Key math concepts include circle area formula, polygon area, limit theory, and geometric transformations. Construction involves commands like Intersect, Circle, Segment, Sequence, Rotate, OrthogonalLine, and Area. Suitable for high school mathematics education, illustrating limits and approximation techniques.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Segment(A, B) → b
  4. Sequence(Rotate[B, ((2 * π / sides) * i), A], i, 0, sides) → list1
  5. Sequence(Segment[Element[list1, i], Element[list1, i + 1]], i, 0, sides) → list2
  6. Rotate(B, (2 * π / sides), A) → B'
  7. Segment(B', B) → d
  8. OrthogonalLine(A, d) → e
  9. Intersect(e, d) → D
  10. Circle(A, D) → f
  11. Segment(A, D) → g
  12. Sequence(Rotate[D, ((2 * π / sides) * i), A], i, 0, sides) → list3
  13. Sequence(Segment[Element[list3, i], Element[list3, i + 1]], i, 0, sides) → list4
  14. Segment(A, B) → a
  15. Segment(A, D) → h
  16. Area(f) → i