Arithmetic vs Geometric Mean Demo

Arithmetic vs Geometric Mean Demo
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2017-04-06 05:46
This example dynamically demonstrates the relationship and difference between arithmetic and geometric means. Key math concepts include arithmetic mean, geometric mean, inequality relations, sequences, and function graphing. Construction highlights involve using GeoGebra commands like Segment, Line, Point, Midpoint, Semicircle, OrthogonalLine, Intersect, Angle, CircleArc to build geometric models, with sliders for parameter variation. Suitable for high school and above learners to understand the mean inequality and its applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(A, B) → g
  3. Point(g) → C
  4. Segment(B, C) → b
  5. Midpoint(A, C) → D
  6. Semicircle(A, C) → c
  7. OrthogonalLine(D, g) → f
  8. Intersect(c, f, 1) → E
  9. OrthogonalLine(B, g) → h
  10. Intersect(c, h, 1) → F
  11. Angle(F, B, A) → α
  12. Angle(E, D, A) → β
  13. Segment(E, D) → i
  14. Segment(B, F) → j
  15. Segment(M, D) → l
  16. CircleArc(D, C, M) → d
  17. Segment(B, N) → m