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Limited Growth

Limited Growth
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2016-07-13 05:24
Geometric Construction
In collections ICME 13, TSG 46: Growth and Modelling with KUMULATOR
This example demonstrates the mathematical model of limited growth; core concepts include arithmetic, congruence, similar triangles, mode, and rhombus; construction highlights from the summary involve commands/objects like Textfield, LaTeX, First, PolyLine, Element, Polygon, Segment, Sequence, If; suitable for high school mathematics teaching, demonstrating and exploring limited growth models.

GeoGebra Commands & Parameters

  1. Textfield(ST) → TxtST
  2. Textfield(ET) → TxtET
  3. Textfield(SA) → TxtSA
  4. Textfield(SB) → TxtSB
  5. Textfield(SC) → TxtSC
  6. Textfield(vA) → TxtvA
  7. Textfield(vB) → TxtvB
  8. Textfield(vC) → TxtvC
  9. LaTeX(vA, false, false) → TextvA
  10. LaTeX(vB, false, false) → TextvB
  11. LaTeX(vC, false, false) → TextvC
  12. First(Sequence[(Element[L_T, i + 1], Element[L_A, i + 1]), i, 0, n + 1], Iteration + 1) → L_{TAE}
  13. PolyLine(L_{TAE}) → Str_{AE}
  14. PolyLine(L_{TBE}) → Str_{BE}
  15. PolyLine(L_{TCE}) → Str_{CE}
  16. Element(L_A, Iteration + 1) → Bestand_A
  17. Element(L_B, Iteration + 1) → Bestand_B
  18. Element(L_C, Iteration + 1) → Bestand_C
  19. Element(L_{vA}, Iteration) → Aenderung_A
  20. Element(L_{vB}, Iteration) → Aenderung_B
  21. Element(L_{vC}, Iteration) → Aenderung_C
  22. First(Sequence[(Element[L_T, i + 1], Element[L_{vA}, i + 1]), i, 0, n], Iteration) → L_{TvAE}
  23. PolyLine(L_{TvAE}) → Str_{vAE}
  24. PolyLine(L_{TvBE}) → Str_{vBE}
  25. PolyLine(L_{TvCE}) → Str_{vCE}
  26. Element(L_{TCE}, Iteration) → DrA
  27. Element(L_{TCE}, Iteration + 1) → DrC
  28. Polygon(DrA, DrB, DrC) → Dreieck_C, dr3, dr2, dr1
  29. Element(L_{TvCE}, Iteration) → vCE
  30. Segment(TX, vCE) → Strecke_{vC}
  31. Sequence((Element[L_T, i + 1], Element[L_A, i + 1]), i, 0, n) → L_{TAG}
  32. Sequence((Element[L_T, i + 1], Element[L_{vA}, i + 1]), i, 0, n - 1) → L_{TvAG}
  33. If(b, 1, 5) → d
  34. PolyLine(L_{TAG}) → Str_{AG}
  35. PolyLine(L_{TvAG}) → Str_{vAG}
  36. PolyLine(L_{TBG}) → Str_{BG}
  37. PolyLine(L_{TvBG}) → Str_{vBG}
  38. PolyLine(L_{TCG}) → Str_{CG}
  39. PolyLine(L_{TvCG}) → Str_{vCG}

AI Drawing Prompt Reference

Draw a geometric diagram illustrating a limited growth model, including three text labels for three changing quantities, three polyline lines showing the trend of these quantities, and three line segments connecting the starting and ending points, finally forming a triangle with three points to demonstrate the properties of similar triangles.
The prompt above was compiled from the original drawing commands and is for reference only.