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Fixed Point Iteration - Find One Root

Fixed Point Iteration - Find One Root
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2018-07-01 18:36
FunctionLimitProbability & StatisticsGraphing
This example demonstrates the fixed point iteration method for finding roots of an equation. Key mathematical concepts include fixed points, iteration, and the existence of roots. Using GeoGebra commands such as Segment, Intersect, and Textfield, the process of iteration and the movement of points are dynamically illustrated. Suitable for high school mathematics education, particularly for learning numerical methods and equation solving.

GeoGebra Commands & Parameters

  1. Segment((B2, B2), (B2, C2)) → D2
  2. Segment((B2, C2), (C2, C2)) → E2
  3. Segment((B3, B3), (B3, C3)) → D3
  4. Segment((B4, B4), (B4, C4)) → D4
  5. Segment((B5, B5), (B5, C5)) → D5
  6. Segment((B6, B6), (B6, C6)) → D6
  7. Segment((B7, B7), (B7, C7)) → D7
  8. Segment((B8, B8), (B8, C8)) → D8
  9. Segment((B9, B9), (B9, C9)) → D9
  10. Segment((B10, B10), (B10, C10)) → D10
  11. Segment((B11, B11), (B11, C11)) → D11
  12. Segment((B12, B12), (B12, C12)) → D12
  13. Segment((B3, C3), (C3, C3)) → E3
  14. Segment((B4, C4), (C4, C4)) → E4
  15. Segment((B5, C5), (C5, C5)) → E5
  16. Segment((B6, C6), (C6, C6)) → E6
  17. Segment((B7, C7), (C7, C7)) → E7
  18. Segment((B8, C8), (C8, C8)) → E8
  19. Segment((B9, C9), (C9, C9)) → E9
  20. Segment((B10, C10), (C10, C10)) → E10
  21. Segment((B11, C11), (C11, C11)) → E11
  22. Segment((B12, C12), (C12, C12)) → E12
  23. Segment((B2, 0), (B2, g(B2))) → G2
  24. Segment((B3, 0), (B3, g(B3))) → G3
  25. Segment((B4, 0), (B4, g(B4))) → G4
  26. Segment((B5, 0), (B5, g(B5))) → G5
  27. Intersect(a, D2) → Start
  28. Segment((B6, 0), (B6, g(B6))) → G6
  29. Segment((B7, 0), (B7, g(B7))) → G7
  30. Segment((B8, 0), (B8, g(B8))) → G8
  31. Segment((B9, 0), (B9, g(B9))) → G9
  32. Segment((B10, 0), (B10, g(B10))) → G10
  33. Segment((B11, 0), (B11, g(B11))) → G11
  34. Segment((B12, 0), (B12, g(B12))) → G12
  35. Textfield(f) → InputBox1
  36. Textfield(g) → InputBox2

AI Drawing Prompt Reference

Draw the graph of function f(x) and its fixed point iteration form g(x). Use the fixed point iteration method to find the root of the equation. First, draw the graphs of f(x) and g(x). Then, draw line segments from the x-axis to the graph of g(x) to represent each iteration step. Next, find the intersection point to determine the starting point of the iteration and draw line segments from the x-axis to the graph of g(x) to show each iteration step.
The prompt above was compiled from the original drawing commands and is for reference only.