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Area of Circle -- Dissection

Area of Circle -- Dissection
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2017-12-22 21:52
CircleTrigonometryGeometric Construction
In collections Mathematics Form 2
This example demonstrates how to calculate the area of a circle by dissecting it. Key mathematical concepts include the area formula of a circle and geometric construction. It uses commands such as If, Div, Line, Point, Distance, Sequence, Rotate, CircleSector, Vector, Translate, Circle, Zip, Segment, Intersect, CircleArc, Midpoint, OrthogonalLine, LineBisector, Semicircle, Angle, and SelectedIndex in GeoGebra. Suitable for middle school and above students to learn the method of calculating the area of a circle.

GeoGebra Commands & Parameters

  1. If(r ≤ 1, 0, r - 1) → r_2
  2. Div(n, 2) → BNum
  3. Line(A, yAxis) → g
  4. Point(g) → O
  5. Distance(A, O) → OA
  6. Sequence((x(A) + (t * HPj), y(A)), t, 1, CurSector) → ListH
  7. Sequence((x(A) + (0.5 * HPj) + (t * HPj), y(A) + VPj), t, 0, CurSector - 1) → ListV
  8. Rotate(SP4b, α / 2, SP4a) → F
  9. CircleSector(SP4a, F, SP4c) → TSektor2
  10. If(b > 1, 1, b) → k
  11. Rotate(O, (((-k) * α)) / 2, A) → SP1a
  12. Rotate(A, α, O) → SP0
  13. Rotate(SP0, (((-k) * α)) / 2, A) → SP1b
  14. Vector(A, SP1b) → v
  15. Translate(SP1b, Vector[((CurSector - 1) * v)]) → SP2c
  16. Translate(SP1a, Vector[((CurSector - 1) * v)]) → SP2a
  17. Rotate(A, (0.5 * α), O) → SP0b
  18. Rotate(A, (1.5 * α), O) → SP0a
  19. Line(A, xAxis) → f
  20. Circle(O, A) → c
  21. Rotate(SP2a, ((-h) * α), ListH(CurSector)) → SP3a
  22. Rotate(SP2c, α, SP2a) → SP2b
  23. Rotate(SP2b, ((-h) * α), ListH(CurSector)) → SP3b
  24. Zip(CircleSector[p, q, r], p, Take[ListV, 2], q, ListH, r, Take[ListH, 2]) → ListHSector
  25. Sequence(Rotate[SP1b, (p * α), SP1a], p, 1, n - 1) → ListPSector1
  26. Zip(CircleSector[SP1a, p, q], p, Append[SP1b, ListPSector1], q, ListPSector1) → ListCSector1
  27. Sequence(Rotate[SP3b, (p * α), SP3a], p, 1, n - CurSector - 1) → ListPSector2
  28. Zip(CircleSector[SP3a, p, q], p, Append[SP3b, ListPSector2], q, ListPSector2) → ListCSector2
  29. Segment(O, A) → i
  30. If(b ≟ n, true, false) → IsMax
  31. Circle(A, Jejari) → d
  32. Intersect(d, g, 2) → C
  33. Rotate(A, β, C) → D
  34. CircleArc(C, A, D) → e
  35. Circle(A, ((2 * π) * OA)) → p
  36. Midpoint(O, A) → E
  37. OrthogonalLine(O, g) → m
  38. CircleSector(SP2a, SP2c, SP2b) → Sektor2
  39. CircleSector(SP1a, A, SP1b) → Sektor1
  40. Zip(CircleSector[p, q, r], p, Take[ListV, 2, BNum], q, Take[ListH, 1, BNum - 1], r, Take[ListH, 2, BNum]) → ListASector1
  41. Zip(CircleSector[p, q, r], p, Take[ListV, BNum + 2], q, Take[ListH, BNum + 1], r, Take[ListH, BNum + 2]) → ListASector2
  42. If(Genap ≟ true, Midpoint[SP4a, SP4b], Midpoint[SP4a, SP4c]) → Pt1
  43. OrthogonalLine(SP4a, f) → Tengah
  44. CircleSector(SP4a, SP4b, F) → TSektor1
  45. Intersect(p, f) → G, B
  46. Segment(A, B) → j
  47. If(r > 1, 1, r) → r_1
  48. Circle(O, A) → c_1
  49. Midpoint(A, B) → M
  50. CircleSector(SP4a, SP4b, SP4c) → ASektor1
  51. Rotate(SP4a, α / 2, SP4b) → H
  52. CircleSector(SP4b, H, SP4d) → ASektor1a
  53. CircleSector(SP4b, SP4a, H) → ASektor1b
  54. Rotate(ListASector2, ((r_1 * 180))°, Pt1) → ListRASector
  55. Rotate(ASektor1, ((r_1 * 180))°, Pt1) → ARSektor1
  56. Rotate(F, ((r_1 * 180))°, Pt1) → F'
  57. Rotate(SP4a, ((r_1 * 180))°, Pt1) → J
  58. Segment(J, F') → f_1
  59. LineBisector(A, SP4a) → g_1
  60. LineBisector(SP4c, O) → h_1
  61. Intersect(g_1, h_1) → I
  62. Rotate(TSektor2, (r_2 * (180° - α / 2)), I) → TRSektor2
  63. Semicircle(A, SP4b) → s
  64. Midpoint(A, SP4b) → K
  65. Rotate(SP4b, ((r_2 * 180))°, K) → SP4e
  66. Vector(SP4b, SP4e) → t
  67. Translate(ASektor1b, t) → ATSektor1b
  68. Rotate(Sektor2, ((-h) * α), ListH(CurSector)) → Sektor3
  69. Point(f) → L
  70. Angle(O, A, L) → γ
  71. SelectedIndex(Bahasa) → nn
  72. If(nn ≟ 1, "r", "j") → text1

AI Drawing Prompt Reference

Draw a circle with center O and radius OA, then divide it into multiple sectors to demonstrate how to calculate its area by dissecting it. First, draw the circle with center O and radius OA. Then, use rotation and translation operations to divide the circle into multiple sectors, and finally show how these sectors combine to form the entire circle.
The prompt above was compiled from the original drawing commands and is for reference only.