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Geometric Mean Demonstration by davidcorcoran

Geometric Mean Demonstration by davidcorcoran
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2019-02-15 01:22
Coordinate GeometryOptimizationGeometric Construction
This example dynamically demonstrates how to calculate the geometric mean by constructing segments and angles. It involves core mathematical concepts such as the definition of the geometric mean, segment length calculation, angle measurement, and potential optimization problems. The construction uses GeoGebra commands/objects like Segment, Angle, and various labeled objects (a, b, c, ..., α, β, A_1, B_2, etc.). Suitable for high school mathematics education to understand the practical application and construction method of the geometric mean.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(B, D) → h
  4. Segment(A, E) → i
  5. Segment(E, D) → j
  6. Segment(E, D) → k
  7. Segment(E, D) → l
  8. Angle(A, B, D) → α
  9. Segment(E, C) → m
  10. Angle(C, E, A) → β
  11. Segment(A_1, B_1) → f_1
  12. Segment(B_1, C_1) → g_1
  13. Segment(B_1, D_1) → h_1
  14. Segment(A_1, E_1) → i_1
  15. Segment(E_1, D_1) → j_1
  16. Segment(E_1, D_1) → k_1
  17. Segment(E_1, D_1) → l_1
  18. Angle(A_1, B_1, D_1) → α_1
  19. Segment(E_1, C_1) → m_1
  20. Angle(C_1, E_1, A_1) → β_1
  21. Angle(A_1, B_1, D_1) → γ
  22. Angle(A_1, E_1, C_1) → δ
  23. Segment(A_2, B_2) → f_2
  24. Segment(B_2, C_2) → g_2
  25. Segment(B_2, D_2) → h_2
  26. Segment(A_2, E_2) → i_2
  27. Segment(E_2, D_2) → j_2
  28. Segment(E_2, D_2) → k_2
  29. Segment(E_2, D_2) → l_2
  30. Angle(A_2, B_2, D_2) → α_2
  31. Segment(E_2, C_2) → m_2
  32. Angle(C_2, E_2, A_2) → β_2