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Bisection Method to Find a Real Root of an Equation

Bisection Method to Find a Real Root of an Equation
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2019-04-12 09:14
FunctionCalculusGeometric Construction
This example demonstrates the bisection method for finding a real root of an equation. Key mathematical concepts include functions, intervals, midpoints, and convergence. The construction involves functions, interval division, midpoint calculation, and iterative processes. GeoGebra commands used include Point, Line, Intersect, Segment, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. SelectedElement(Function) → f
  4. If((B2 * D2) < 0, true, false) → G2
  5. If(G2, A2, C2) → A3
  6. If(G2, C2, E2) → E3
  7. If((B3 * D3) < 0, true, false) → G3
  8. If(G3, A3, C3) → A4
  9. If(G3, C3, E3) → E4
  10. If((B4 * D4) < 0, true, false) → G4
  11. If(G4, A4, C4) → A5
  12. If(G4, C4, E4) → E5
  13. If((B5 * D5) < 0, true, false) → G5
  14. If(G5, A5, C5) → A6
  15. If(G5, C5, E5) → E6
  16. If((B6 * D6) < 0, true, false) → G6
  17. If(G6, A6, C6) → A7
  18. If(G6, C6, E6) → E7
  19. If((B7 * D7) < 0, true, false) → G7
  20. If(G7, A7, C7) → A8
  21. If(G7, C7, E7) → E8
  22. If((B8 * D8) < 0, true, false) → G8
  23. If(G8, A8, C8) → A9
  24. If(G8, C8, E8) → E9
  25. If((B9 * D9) < 0, true, false) → G9
  26. If(G9, A9, C9) → A10
  27. If(G9, C9, E9) → E10
  28. If((B10 * D10) < 0, true, false) → G10
  29. If(G10, A10, C10) → A11
  30. If(G10, C10, E10) → E11
  31. If((B11 * D11) < 0, true, false) → G11
  32. If(G11, A11, C11) → A12
  33. If(G11, C11, E11) → E12
  34. If((B12 * D12) < 0, true, false) → G12
  35. If(G12, A12, C12) → A13
  36. If(G12, C12, E12) → E13
  37. If((B13 * D13) < 0, true, false) → G13
  38. If(G13, A13, C13) → A14
  39. If(G13, C13, E13) → E14
  40. If((B14 * D14) < 0, true, false) → G14
  41. If(G14, A14, C14) → A15
  42. If(G14, C14, E14) → E15
  43. If((B15 * D15) < 0, true, false) → G15
  44. If(G15, A15, C15) → A16
  45. If(G15, C15, E15) → E16
  46. If((B16 * D16) < 0, true, false) → G16
  47. If(G16, A16, C16) → A17
  48. If(G16, C16, E16) → E17
  49. If((B17 * D17) < 0, true, false) → G17
  50. If(G17, A17, C17) → A18
  51. If(G17, C17, E17) → E18
  52. If((B18 * D18) < 0, true, false) → G18
  53. If(G18, A18, C18) → A19
  54. If(G18, C18, E18) → E19
  55. If((B19 * D19) < 0, true, false) → G19
  56. If(G19, A19, C19) → A20
  57. If(G19, C19, E19) → E20
  58. If((B20 * D20) < 0, true, false) → G20
  59. Line(A, xAxis) → a
  60. Line(A, a) → b
  61. OrthogonalLine(A, b) → c
  62. OrthogonalLine(B, b) → d
  63. Intersect(f, c) → C
  64. Intersect(f, d) → D
  65. Segment(D, B) → g
  66. Text(f) → text2
  67. If(e > 0, text4, text1) → text5

AI Drawing Prompt Reference

Draw a function graph to find its intersection with the x-axis. Start by selecting two points A and B on the x-axis, then iteratively narrow down the interval containing the intersection by taking the midpoint of the current interval. If the function value at the midpoint and at point B have opposite signs, the new interval is the midpoint and B; otherwise, it's the midpoint and A. Repeat this process until the interval is sufficiently small.
The prompt above was compiled from the original drawing commands and is for reference only.