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Unit Circle Area Division Demonstration

Unit Circle Area Division Demonstration
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2014-07-29 04:06
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the principle of dividing a unit circle into equal areas using a simple method. It involves core math concepts like area calculation, pi, trigonometric functions, and coordinate geometry. The construction uses GeoGebra commands such as CurveCartesian and objects like A2, n, B2, C2, etc., controlled by a slider n for the number of divisions. Suitable for high school mathematics education to understand circle area properties and geometric constructions.

GeoGebra Commands & Parameters

  1. If(B2 > 3, round(B2 - (B2 * (1 - sqrt(π / B2))^(2))), B2) → C2
  2. If(B3 > 3, round(B3 - (B3 * (1 - sqrt(π / B3))^(2))), B3) → C3
  3. If(B4 > 3, round(B4 - (B4 * (1 - sqrt(π / B4))^(2))), B4) → C4
  4. If(B5 > 3, round(B5 - (B5 * (1 - sqrt(π / B5))^(2))), B5) → C5
  5. If(B6 > 3, round(B6 - (B6 * (1 - sqrt(π / B6))^(2))), B6) → C6
  6. If(B7 > 3, round(B7 - (B7 * (1 - sqrt(π / B7))^(2))), B7) → C7
  7. If(B8 > 3, round(B8 - (B8 * (1 - sqrt(π / B8))^(2))), B8) → C8
  8. If(B9 > 3, round(B9 - (B9 * (1 - sqrt(π / B9))^(2))), B9) → C9
  9. If(B10 > 3, round(B10 - (B10 * (1 - sqrt(π / B10))^(2))), B10) → C10
  10. If(B11 > 3, round(B11 - (B11 * (1 - sqrt(π / B11))^(2))), B11) → C11
  11. If(B12 > 3, round(B12 - (B12 * (1 - sqrt(π / B12))^(2))), B12) → C12
  12. If(B13 > 3, round(B13 - (B13 * (1 - sqrt(π / B13))^(2))), B13) → C13
  13. If(B14 > 3, round(B14 - (B14 * (1 - sqrt(π / B14))^(2))), B14) → C14
  14. If(B15 > 3, round(B15 - (B15 * (1 - sqrt(π / B15))^(2))), B15) → C15
  15. If(B16 > 3, round(B16 - (B16 * (1 - sqrt(π / B16))^(2))), B16) → C16
  16. CurveCartesian((A3 * cos(((2 * π) * t))), (A3 * sin(((2 * π) * t))), t, 0, 1) → D3
  17. CurveCartesian((A2 * cos(((2 * π) * t))), (A2 * sin(((2 * π) * t))), t, 0, 1) → D2
  18. CurveCartesian((A4 * cos(((2 * π) * t))), (A4 * sin(((2 * π) * t))), t, 0, 1) → D4
  19. CurveCartesian((A5 * cos(((2 * π) * t))), (A5 * sin(((2 * π) * t))), t, 0, 1) → D5
  20. CurveCartesian((A6 * cos(((2 * π) * t))), (A6 * sin(((2 * π) * t))), t, 0, 1) → D6
  21. CurveCartesian((A7 * cos(((2 * π) * t))), (A7 * sin(((2 * π) * t))), t, 0, 1) → D7
  22. CurveCartesian((A8 * cos(((2 * π) * t))), (A8 * sin(((2 * π) * t))), t, 0, 1) → D8
  23. CurveCartesian((A9 * cos(((2 * π) * t))), (A9 * sin(((2 * π) * t))), t, 0, 1) → D9
  24. CurveCartesian((A10 * cos(((2 * π) * t))), (A10 * sin(((2 * π) * t))), t, 0, 1) → D10
  25. If(B2 > 1, Sequence[Segment[D2(s / C2), D3(s / C2)], s, 1, C2]) → E2
  26. If(B3 > 1, Sequence[Segment[D3(s / C3), D4(s / C3)], s, 1, C3]) → E3
  27. If(B4 > 1, Sequence[Segment[D4(s / C4), D5(s / C4)], s, 1, C4]) → E4
  28. If(B5 > 1, Sequence[Segment[D5(s / C5), D6(s / C5)], s, 1, C5]) → E5
  29. If(B6 > 1, Sequence[Segment[D6(s / C6), D7(s / C6)], s, 1, C6]) → E6
  30. If(B7 > 1, Sequence[Segment[D7(s / C7), D8(s / C7)], s, 1, C7]) → E7
  31. If(B8 > 1, Sequence[Segment[D8(s / C8), D9(s / C8)], s, 1, C8]) → E8
  32. If(B9 > 1, Sequence[Segment[D9(s / C9), D10(s / C9)], s, 1, C9]) → E9
  33. CurveCartesian((A11 * cos(((2 * π) * t))), (A11 * sin(((2 * π) * t))), t, 0, 1) → D11
  34. CurveCartesian((A12 * cos(((2 * π) * t))), (A12 * sin(((2 * π) * t))), t, 0, 1) → D12
  35. CurveCartesian((A13 * cos(((2 * π) * t))), (A13 * sin(((2 * π) * t))), t, 0, 1) → D13
  36. If(B10 > 1, Sequence[Segment[D10(s / C10), D11(s / C10)], s, 1, C10]) → E10
  37. If(B11 > 1, Sequence[Segment[D11(s / C11), D12(s / C11)], s, 1, C11]) → E11
  38. If(B12 > 1, Sequence[Segment[D12(s / C12), D13(s / C12)], s, 1, C12]) → E12
  39. CurveCartesian((A14 * cos(((2 * π) * t))), (A14 * sin(((2 * π) * t))), t, 0, 1) → D14
  40. CurveCartesian((A15 * cos(((2 * π) * t))), (A15 * sin(((2 * π) * t))), t, 0, 1) → D15
  41. CurveCartesian((A16 * cos(((2 * π) * t))), (A16 * sin(((2 * π) * t))), t, 0, 1) → D16
  42. If(B17 > 3, round(B17 - (B17 * (1 - sqrt(π / B17))^(2))), B17) → C17
  43. CurveCartesian((A17 * cos(((2 * π) * t))), (A17 * sin(((2 * π) * t))), t, 0, 1) → D17
  44. If(B13 > 1, Sequence[Segment[D13(s / C13), D14(s / C13)], s, 1, C13]) → E13
  45. If(B14 > 1, Sequence[Segment[D14(s / C14), D15(s / C14)], s, 1, C14]) → E14
  46. If(B15 > 1, Sequence[Segment[D15(s / C15), D16(s / C15)], s, 1, C15]) → E15
  47. If(B16 > 1, Sequence[Segment[D16(s / C16), D17(s / C16)], s, 1, C16]) → E16

AI Drawing Prompt Reference

Draw a unit circle and divide it into multiple areas. First, use pi and trigonometric functions to calculate the radius and angle for each area. Then, draw the boundaries of each area using curves. Finally, connect the boundary points of adjacent areas with line segments to form multiple sector areas.
The prompt above was compiled from the original drawing commands and is for reference only.