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Area of a Circle - Wedge Demo

Area of a Circle - Wedge Demo
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2020-02-04 09:07
CircleSequenceGeometric Construction
This example visually demonstrates the sector-proof of the area of a circle. Key mathematical concepts include the area formula of a circle and its proof. It uses Polygon, Circle, Point, Rotate, Segment, Midpoint, Sequence, and other GeoGebra commands. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (base, 0), (base, r), (0, r)) → poly1, a, b, c, d
  2. Circle(A, r) → e
  3. Point(e) → B
  4. Rotate(B, 360 * ° / n, A) → B'
  5. Segment(B, B') → dx
  6. Midpoint(dx) → C
  7. Segment(A, C) → dy
  8. Sequence(Rotate[B, j * 360 * ° / n, A], j, 0, n) → list1
  9. Sequence(CircleSector[A, Element[list1, j], Element[list1, j + 1]], j, 1, n, 2) → list2
  10. Sequence(CircleSector[A, Element[list1, j], Element[list1, j + 1]], j, 2, n, 2) → list3
  11. Sequence(CircleSector[(j * dx, 0), (j * dx + dx / 2, dy), (j * dx + (-dx) / 2, dy)], j, 0, n / 2 - 1) → list4
  12. Sequence(CircleSector[(j * dx + dx / 2, dy), (j * dx + 0, 0), (j * dx + dx, 0)], j, 0, n / 2 - 1) → list5

AI Drawing Prompt Reference

Draw a circle with a point at one vertex of a rectangle, where the radius equals the side length of the rectangle. Then rotate this point around the circle's center to form multiple sectors, which will approximate the area of the circle.
The prompt above was compiled from the original drawing commands and is for reference only.