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Calculating the Area of a Circle by minoomath

Calculating the Area of a Circle by minoomath
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2014-03-03 02:34
CircleAngleVectorGeometric Construction
This example demonstrates how to derive the formula for the area of a circle using rotation and sector area calculations. It involves core mathematical concepts such as circle, sector, angle, rotation, vector, and more. The construction uses GeoGebra commands/objects like Circle, Rotate, CircleSector, Angle, Sequence, Point, OrthogonalLine, Vector, Midpoint, Mirror. Suitable for middle school students and above to learn and understand the geometric meaning of the circle area formula, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Circle(A, p) → c
  2. Rotate(B, (360 / n)°, A) → B'
  3. CircleSector(A, B, B') → d
  4. Angle(B, A, B') → α
  5. Sequence(Rotate[d, 360° - (i * 360 / n)°, A], i, 1, n, 1) → list1
  6. Point(xAxis) → C
  7. OrthogonalLine(C, xAxis) → a
  8. Circle(C, p) → e
  9. Rotate(B, 225*°, A) → B'_1
  10. Rotate(B', 225*°, A) → B''
  11. Rotate(D, (-α) / 2, C) → D'
  12. Rotate(C, α, D') → C'
  13. CircleSector(D', C, C') → f
  14. Vector(C, C') → u
  15. Midpoint(D', C') → E
  16. Sequence(Translate[f, Vector[i / 2 * u]], i, 2, n, 2) → list2
  17. Mirror(f, E) → f'
  18. Sequence(Translate[f', Vector[i / 2 * u]], i, 2, n, 2) → list3