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Cobweb Slope

Cobweb Slope
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2014-02-23 19:19
FunctionOptimizationInequality
This example demonstrates the effect of slope on the attracting property of a fixed point. Key mathematical concepts include functions, fixed points, and slopes. Using commands like Point, OrthogonalLine, and Segment from the construction summary, a cobweb diagram can be drawn. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A0
  2. OrthogonalLine(A0, xAxis) → a
  3. Point(c) → Fixpoint
  4. Segment((A1, A2), (A2, A2)) → C1
  5. Segment((A2, A2), (A2, A3)) → B2
  6. Segment((A2, A3), (A3, A3)) → C2
  7. Segment((A3, A3), (A3, A4)) → B3
  8. Segment((A3, A4), (A4, A4)) → C3
  9. Segment((A4, A4), (A4, A5)) → B4
  10. Segment((A4, A5), (A5, A5)) → C4
  11. Segment((A5, A5), (A5, A6)) → B5
  12. Segment((A5, A6), (A6, A6)) → C5
  13. Segment((A6, A6), (A6, A7)) → B6
  14. Segment((A6, A7), (A7, A7)) → C6
  15. Segment((A7, A7), (A7, A8)) → B7
  16. Segment((A7, A8), (A8, A8)) → C7
  17. Segment((A8, A8), (A8, A9)) → B8
  18. Segment((A8, A9), (A9, A9)) → C8
  19. Segment((A9, A9), (A9, A10)) → B9
  20. Segment((A9, A10), (A10, A10)) → C9
  21. Segment((A10, A10), (A10, A11)) → B10
  22. Segment((A10, A11), (A11, A11)) → C10
  23. Segment((A11, A11), (A11, A12)) → B11
  24. Segment((A11, A12), (A12, A12)) → C11
  25. Segment((A12, A12), (A12, A13)) → B12
  26. Segment((A12, A13), (A13, A13)) → C12
  27. Segment((A13, A13), (A13, A14)) → B13
  28. Segment((A13, A14), (A14, A14)) → C13
  29. Segment((A14, A14), (A14, A15)) → B14
  30. Segment((A14, A15), (A15, A15)) → C14
  31. Segment((A15, A15), (A15, A16)) → B15
  32. Segment((A15, A16), (A16, A16)) → C15
  33. Segment((A16, A16), (A16, A17)) → B16
  34. Segment((A16, A17), (A17, A17)) → C16
  35. Segment((A17, A17), (A17, A18)) → B17
  36. Segment((A17, A18), (A18, A18)) → C17
  37. Segment((A18, A18), (A18, A19)) → B18
  38. Segment((A18, A19), (A19, A19)) → C18
  39. Segment((A19, A19), (A19, A20)) → B19
  40. Segment((A19, A20), (A20, A20)) → C19
  41. Segment((A20, A20), (A20, A21)) → B20
  42. Segment((A20, A21), (A21, A21)) → C20
  43. Segment((A21, A21), (A21, A22)) → B21
  44. Segment((A21, A22), (A22, A22)) → C21
  45. Segment((A1, 0), (A1, A2)) → b

AI Drawing Prompt Reference

Draw a cobweb diagram for a function's attracting point. Start by taking a point A0 on the x-axis and drawing a perpendicular line a through A0. Then, take a fixed point Fixpoint on line a and draw a series of vertical segments, each starting from the end of the previous segment and ending on the x-axis, forming a spiderweb-like structure to illustrate the effect of the function's slope on the attracting point.
The prompt above was compiled from the original drawing commands and is for reference only.