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Area of a Circle by Anthony Dove

Area of a Circle by Anthony Dove
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2020-09-24 02:21
CircleFunctionGeometric Construction
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 Sequence, Point, OrthogonalLine, Mirror, Intersect, Vector, If, Segment, Line, and Polygon in GeoGebra. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Sequence((((2 * i) - 1) * a), i, 1, n) → angles
  2. Sequence(Vector[(d * Vector[(cos((-Element[angles, i])), sin((-Element[angles, i])))])], i, 1, n) → vectors
  3. Sequence(Midpoint[Cell[2, i], Cell[2, 1 + i]], i, 1, n) → midpoints
  4. Sequence(Intersect[Circle[Cell[2, i], 1], OrthogonalLine[Element[midpoints, i], Line[Cell[2, i], Cell[2, 1 + i]]]], i, 1, n) → lowpoints
  5. Sequence(Mirror[Element[lowpoints, i], yAxis], i, 1, n) → lowpoints2
  6. Sequence(Midpoint[Cell[3, i], Cell[3, 1 + i]], i, 1, n) → midpointsDown
  7. Sequence(Intersect[Circle[Cell[3, i], 1], OrthogonalLine[Element[midpointsDown, i], Line[Cell[3, i], Cell[3, 1 + i]]]], i, 1, n) → uppoints
  8. Sequence(Mirror[Element[uppoints, i], yAxis], i, 1, n) → uppoints2
  9. Point(yAxis) → B
  10. OrthogonalLine(B, yAxis) → g
  11. Point(g) → C
  12. Mirror(C, yAxis) → C'
  13. Point(h) → D
  14. Mirror(D, (-2, -0.5)) → D'
  15. Intersect(b, xAxis) → E
  16. Intersect(c, h) → F
  17. Intersect(e, g) → G
  18. Intersect(g, f) → H
  19. Vector(D', I) → u
  20. Vector(D, F) → v
  21. Sequence(CircleSector[Element[uppoints, i], Cell[3, 1 + i], Cell[3, i]], i, 1, n, 2) → sectorsDown1
  22. Sequence(CircleSector[Element[uppoints2, i], Mirror[Cell[3, i], yAxis], Mirror[Cell[3, 1 + i], yAxis]], i, 1, n, 2) → sectorsDown3
  23. Sequence(CircleSector[Element[lowpoints, i], Cell[2, 1 + i], Cell[2, i]], i, 1, n, 2) → sectors1
  24. Sequence(CircleSector[Element[lowpoints2, i] + ((2 * x(A)), 0), Mirror[Cell[2, i], yAxis] + ((2 * x(A)), 0), Mirror[Cell[2, 1 + i], yAxis] + ((2 * x(A)), 0)], i, 1, n, 2) → sectors3
  25. Sequence(CircleSector[Element[lowpoints, i], Cell[2, 1 + i], Cell[2, i]], i, 2, n, 2) → sectors2
  26. Sequence(CircleSector[Element[lowpoints2, i] + ((2 * x(A)), 0), Mirror[Cell[2, i], yAxis] + ((2 * x(A)), 0), Mirror[Cell[2, 1 + i], yAxis] + ((2 * x(A)), 0)], i, 2, n, 2) → sectors4
  27. Sequence(CircleSector[Element[uppoints, i], Cell[3, 1 + i], Cell[3, i]], i, 2, n, 2) → sectorsDown2
  28. Sequence(CircleSector[Element[uppoints2, i], Mirror[Cell[3, i], yAxis], Mirror[Cell[3, 1 + i], yAxis]], i, 2, n, 2) → sectorsDown4
  29. If(n ≟ 1, (-0.518, -0.123), If[n ≟ 2, (-1.14, -0.087), If[n ≟ 3, (-1.289, -0.0015), If[n ≟ 4, (-1.38, 0), If[n ≟ 5, (-1.41, 0), If[n ≟ 6, (-1.44, 0), If[n ≟ 7, (-1.46, 0), If[n ≟ 8, (-1.48, 0), If[n ≟ 9, (-1.495, 0), If[n ≟ 10, (-1.505, 0), If[n ≟ 11, (-1.51, 0), If[n ≟ 12, (-1.52, 0), If[n ≟ 13, (-1.523, 0), If[n ≟ 14, (-1.527, 0), If[n ≟ 15, (-1.531, 0), If[n ≟ 16, (-1.535, 0), If[n ≟ 17, (-1.54, 0), If[n ≟ 18, (-1.543, 0), If[n ≟ 19, (-1.546, 0), (-1.55, 0)]]]]]]]]]]]]]]]]]]) → K
  30. If(n ≟ 1, (-1.423, -1), If[n ≟ 2, (-1.539, -1), If[n ≟ 3, (-1.56, -1), (-1.575, -1)]]) → L
  31. Segment(K, L) → l
  32. Line(L, q) → k
  33. If(n ≟ 1, (1.407, -1), If[n ≟ 2, (1.52, -1), If[n ≟ 3, (1.56, -1), (1.571, -1)]]) → J
  34. Line(J, l) → m
  35. Intersect(q, m) → M
  36. Vector(O, P) → p
  37. Vector(Q, R) → w
  38. Polygon(K, M, J, L) → q1, k_1, m_1, j_1, l_1

AI Drawing Prompt Reference

Draw a geometric construction diagram containing circles, points, line segments, and sectors. The diagram includes circles that intersect to form points, which are mirrored to the y-axis, and then connected to line segments and sectors. The construction order is: first draw circles, then intersect to get points, mirror points, and finally draw line segments and sectors. The diagram illustrates the method of calculating the area of a circle.
The prompt above was compiled from the original drawing commands and is for reference only.