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Understanding Circle Area

Understanding Circle Area
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2015-12-19 01:20
CircleGeometric ConstructionSlider Animation
This example guides students to understand the area of a circle as the area of a rectangle with side lengths r and πr, deepening their comprehension of the circle area formula. ①It demonstrates the correlation between the area of a circle and a rectangle. ②Core math concepts include circle area formula, π, rectangle area calculation, and geometric transformations. ③Construction highlights the use of GeoGebra commands: Segment, Circle, Sequence, Vector, CircleSector, Midpoint, Translate, Mirror. ④Suitable for middle school and above students for geometry teaching and concept reinforcement.

GeoGebra Commands & Parameters

  1. Segment(A, B) → r
  2. Circle(A, B) → c
  3. Sequence(Rotate[B, ((360 * i / n))°, A], i, 1, n - 1) → list1
  4. Sequence(Segment[list1(i), A], i, 1, n - 1) → list2
  5. Vector((0, (-2.5 * r))) → u
  6. CircleSector(Translate[A, u], Translate[B, u], Translate[list1(1), u]) → d
  7. Midpoint(r) → C
  8. Translate(C, u) → C'
  9. Mirror(d, C') → d'
  10. Vector(list1(1), B) → v
  11. Sequence(Translate[d, Vector[(v * i)]], i, 1, (n - 1) / 2) → list3
  12. Sequence(Translate[d', Vector[(v * i)]], i, 1, (n - 2) / 2) → list4
  13. CircleSector(A, B, list1(1)) → e