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Linear Growth

Linear Growth
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2016-07-13 05:16
SequenceCoordinate GeometryGeometric Construction
In collections ICME 13, TSG 46: Growth and Modelling with KUMULATOR
This example demonstrates the concept of linear growth within geometric constructions using GeoGebra. It involves core mathematical ideas such as sequences, geometric constructions, and coordinate geometry. Key GeoGebra commands and objects used include Sequence, Textfield, LaTeX, First, PolyLine, Element, Polygon, Segment, and If. Suitable for high school mathematics education, illustrating the application of dynamic geometry and sequences.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a linear growth geometric figure with points A, B, and C, and their changes vA, vB, vC. First, generate a series of points based on the coordinates of A, B, and C, then connect these points to form segments and polygons to illustrate the linear growth process. Finally, draw the changes vA, vB, vC of points A, B, and C, and form new segments and polygons with the original points A, B, and C to show the trend of change.
The prompt above was compiled from the original drawing commands and is for reference only.