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Explore Circumference of Circles

Explore Circumference of Circles
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2015-12-08 08:40
CircleCoordinate GeometryGeometric Construction
This example explores the relationship between the circumference and diameter of circles by measuring different circles' diameters and circumferences. Key mathematical concepts include the circumference formula and proportional relationships. GeoGebra commands used include Point, CurveCartesian, If, Segment, CircleArc, Sequence, Circle, etc. Suitable for middle school and above students to learn basic properties of circles.

GeoGebra Commands & Parameters

  1. Point(yAxis) → B
  2. CurveCartesian((r * (t - sin(t))), (r * (1 - cos(t))) + y(B), t, 0, 6.28319) → f
  3. Point(f) → P
  4. If(x(P) < (r * 3.141592653589793), acos(1 - (y(P) - y(B)) / r), (2 * 3.141592653589793) - acos(1 - (y(P) - y(B)) / r)) → θ
  5. Point(Segment[(x(D0), y(D0) + 0.25), ((r * θ) - r, r + y(B))]) → A
  6. Segment(B, (x(C_1), y(B))) → c1
  7. CircleArc(C_1, (x(C_1), y(B)), P) → c2
  8. CircleArc(C_1, P, (x(C_1), y(B))) → e
  9. Segment(A, (x(A) + (2 * r), y(A))) → j
  10. Sequence(Segment[(((2 * i) * r), 0), (((2 * i) * r), -0.25)], i, 0, 10) → list1
  11. Sequence(Segment[((((2 * i) - 1) * r), 0), ((((2 * i) - 1) * r), -0.2)], i, 1, 10) → list2
  12. Sequence(Sequence[Segment[((i * r) + ((0.2 * j) * r), 0), ((i * r) + ((0.2 * j) * r), -0.15)], j, 1, 4], i, 0, 19) → list3
  13. Segment(B, (x(B) + (20 * r), y(B))) → c
  14. Sequence(Segment[(i, 0), (i, -0.25)], i, 0, 10) → list6
  15. Sequence(Segment[(((2 * i) - 1) / 2, 0), (((2 * i) - 1) / 2, -0.2)], i, 1, 10) → list7
  16. Sequence(Sequence[Segment[(i / 2 + (0.1 * j), 0), (i / 2 + (0.1 * j), -0.15)], j, 1, 4], i, 0, 19) → list8
  17. Sequence(Segment[(((2 * i) - 1) / 20, 0), (((2 * i) - 1) / 20, -0.1)], i, 1, 100) → list10
  18. Sequence(Segment[((((2 * i) - 1) * r / 10), 0), ((((2 * i) - 1) * r / 10), -0.1)], i, 1, 100) → list4
  19. Segment((0, 0), (10, 0)) → a
  20. Sequence(Segment[(((2 * i) - 1) / 200, 0), (((2 * i) - 1) / 200, -0.03)], i, 1, 1000) → list11
  21. Sequence(Sequence[Segment[(i / 20 + (0.01 * j), 0), (i / 20 + (0.01 * j), -0.06)], j, 1, 4], i, 0, 199) → list9
  22. Sequence(Sequence[Segment[((i * r / 10) + ((0.02 * j) * r), 0), ((i * r / 10) + ((0.02 * j) * r), -0.06)], j, 1, 4], i, 0, 199) → list5
  23. Circle((0, r), r) → d
  24. Corner(1) → cor1
  25. Corner(2) → cor2
  26. Corner(3) → cor3
  27. Corner(4) → cor4