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Geometric Mean Demonstration by nicolesusanne29

Geometric Mean Demonstration by nicolesusanne29
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2016-05-19 23:27
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example dynamically demonstrates the concept of the geometric mean, the square root of the product of two segment lengths. It involves core math concepts like geometric mean, quadratic equations, percentages, similarity transformation, cone, and boxplot. GeoGebra commands used include Segment, OrthogonalLine, Point, Angle, Intersect; objects include A, B, AB, g, C, BC, AC, j, α, k, D, β, AD, BD, a_1, b_1, c_1, d_1, text1, text2, b'd'_1, text4, a, c, ac, b, ab, γ, bc, d, a', ad, c', cd, a'c', δ, a', d', a'd', b'. Suitable for high school mathematics teaching to understand the practical application and calculation method of the geometric mean.

GeoGebra Commands & Parameters

  1. Segment(A, B) → AB
  2. OrthogonalLine(A, AB) → g
  3. Point(g) → C
  4. Segment(C, B) → BC
  5. Segment(C, A) → AC
  6. Segment(A, B) → j
  7. Angle(B, A, C) → α
  8. OrthogonalLine(A, BC) → k
  9. Intersect(k, BC) → D
  10. Angle(C, D, A) → β
  11. Segment(A, D) → AD
  12. Segment(B, D) → BD
  13. Point(Circle[a, AC]) → c
  14. Segment(a, c) → ac
  15. Point(Circle[a, AB]) → b
  16. Segment(a, b) → ab
  17. Angle(b, a, c) → γ
  18. Segment(c, b) → bc
  19. Point(Circle[d, AD]) → a'
  20. Segment(d, a') → ad
  21. Point(Circle[d, Distance[C, D]]) → c'
  22. Segment(d, c') → cd
  23. Segment(a', c') → a'c'
  24. Angle(c', d, a') → δ
  25. Point(Circle[a'', AD]) → d''
  26. Segment(a'', d'') → a''d''
  27. Point(Circle[d'', BD]) → b'
  28. Segment(d'', b') → b'd''
  29. Segment(a'', b') → a''b'
  30. Angle(b', d'', a'') → ε