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Area of Circles

Area of Circles
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2014-01-08 12:01
CircleFunctionGeometric Construction
In collections Measurement
This example demonstrates how to calculate the area of a circle using geometric construction. Key mathematical concepts include the properties of circles and the area formula. It utilizes commands such as circle, intersection, text field, segment, point, vector, translate, midpoint, sequence, etc. Suitable for middle school and above students to learn geometry and area calculation.

GeoGebra Commands & Parameters

  1. If(s ≤ 1.5, 0, If[(1.5 < s) ∧ (s ≤ 2.5), s - 1.5, 1]) → s2
  2. Intersect(yAxis, xAxis) → O
  3. Circle(A, O) → c
  4. Circumference(c) → z
  5. If(s ≤ 5, 0, If[(5 < s) ∧ (s ≤ 6), s - 5, 1]) → s5
  6. If(s ≤ 3, 0, If[(3 < s) ∧ (s ≤ 4), s - 3, 1]) → s3
  7. If(s ≤ 4, 0, If[(4 < s) ∧ (s ≤ 5), s - 4, 1]) → s4
  8. If(s ≤ 0, 0, If[(0 < s) ∧ (s ≤ 1), s, 1]) → s1
  9. Textfield(A1) → dv1
  10. Segment(O, M) → b
  11. Circle(A, O) → d
  12. Point(yAxis) → H
  13. Vector(O, H) → z_1
  14. Translate(M, z_1) → M'
  15. Vector(H, M') → e
  16. Vector(M', H) → t
  17. Midpoint(H, M') → I
  18. Vector(J, K) → h
  19. Vector(K, J) → R
  20. Segment(M', M) → j
  21. Segment(H, O) → k
  22. Segment(O, J) → l
  23. Segment(A, K) → p
  24. Midpoint(K, J) → P
  25. If(s ≤ 6, 0, If[(6 < s) ∧ (s ≤ 7), s - 6, 1]) → s6
  26. If(s ≤ 7, 0, If[(7 < s) ∧ (s ≤ 8), s - 7, 1]) → s7
  27. Circle(A, O) → q
  28. Sequence(Dilate[O, i / n, A], i, 0, n) → Li1
  29. CircleArc(C, O, B) → s_1
  30. Sequence(Dilate[B, i / n, A], i, 0, n) → Li2
  31. Sequence(Dilate[C, i / n, A], i, 0, n) → Li3
  32. Sequence(CircleArc[Element[Li3, i], Element[Li1, i], Element[Li2, i]], i, 1, n) → Li4
  33. Sequence(Dilate[M, i / n, A], i, 0, n) → Li5
  34. Sequence(Segment[Element[Li1, i], Element[Li5, i]], i, 1, n) → Li6
  35. Segment(A, M) → r
  36. CircleArc(C', O, B') → s_2
  37. Sequence(Circle[A, Element[Li1, i]], i, 1, n) → Li7
  38. Sequence(CircleArc[A, Rotate[Element[Li1, i], (((-360))° * s2), A], Element[Li1, i]], i, 1, n) → Li8

AI Drawing Prompt Reference

Draw a circle with its center labeled and the area formula displayed. From the center, draw a ray and place multiple points along it. Using these points, draw several concentric circles to illustrate the area calculation process. Use different colors and line styles to distinguish parts, and label key points with names and values for clarity.
The prompt above was compiled from the original drawing commands and is for reference only.