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Balancing Equations Through Geometric Construction

Balancing Equations Through Geometric Construction
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2020-07-26 17:35
FunctionTransformationGeometric Construction
This example demonstrates how to maintain equation balance through geometric construction. Key mathematical concepts include equation balance and transformation. GeoGebra commands used include If, Max, Segment, Rotate, Textfield, and Sequence. Suitable for middle school mathematics education.

GeoGebra Commands & Parameters

  1. If(LV ≟ 0 ∧ RV ≟ 0, 0, (LV - RV) / (LV + RV)) → Tilt
  2. Max(LN, RN) → mxn
  3. Segment(A, B) → f
  4. Rotate(D, α, A) → D'
  5. Textfield(LT_1) → LT
  6. Textfield(LS_1) → LS
  7. Textfield(RT_1) → RT
  8. Textfield(RS_1) → RS
  9. Textfield(LC_1) → LC
  10. Textfield(RC_1) → RC
  11. Textfield(CV) → VC
  12. Textfield(TV) → VT
  13. Textfield(SV) → VS
  14. Rotate(E, α, A) → E'
  15. Segment(E', D') → k
  16. Sequence(Segment[E' + ((i - 1) * (0, (-1.5 * lng))), E' + ((i - 1) * (0, (-1.5 * lng))) + (0, (-0.5 * lng))], i, 1, LN) → list1
  17. Sequence(trw[E' + (0, (-0.5 * lng)) + ((i - 1) * (0, (-1.5 * lng))), lng], i, 1, LT_1) → LTlist
  18. Sequence(sqw[E' + (0, (-0.5 * lng)) + ((i - 1) * (0, (-1.5 * lng))), lng], i, 1 + LT_1, LT_1 + LS_1) → LSlist
  19. Sequence(crc[E' + (0, (-0.5 * lng)) + ((i - 1) * (0, (-1.5 * lng))), lng], i, 1 + LT_1 + LS_1, LN) → LClist
  20. Sequence(Segment[D' + ((i - 1) * (0, (-1.5 * lng))), D' + ((i - 1) * (0, (-1.5 * lng))) + (0, (-0.5 * lng))], i, 1, RN) → list2
  21. Sequence(trw[D' + (0, (-0.5 * lng)) + ((i - 1) * (0, (-1.5 * lng))), lng], i, 1, RT_1) → RTlist
  22. Sequence(sqw[D' + (0, (-0.5 * lng)) + ((i - 1) * (0, (-1.5 * lng))), lng], i, RT_1 + 1, RT_1 + RS_1) → RSlist
  23. Sequence(crc[D' + (0, (-0.5 * lng)) + ((i - 1) * (0, (-1.5 * lng))), lng], i, 1 + RT_1 + RS_1, RN) → RClist