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Arithmetic Mean Demonstration

Arithmetic Mean Demonstration
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2019-08-10 01:18
FunctionTrigonometryCoordinate GeometryOptimizationGeometric Construction
This example demonstrates the geometric meaning of the arithmetic mean, constructing the position of the mean through a semicircle and perpendicular lines; involves core concepts like arithmetic mean, continuity, trigonometric functions, stochastic processes, trapezoids, and power functions; construction highlights include commands/objects like Point, Semicircle, Midpoint, OrthogonalLine, Mirror, Intersect, Segment; suitable for high school mathematics teaching to understand the intuitive representation and geometric properties of the arithmetic mean.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Point(xAxis) → D
  5. Point(xAxis) → E
  6. Point(xAxis) → F
  7. Point(xAxis) → G
  8. Point(xAxis) → H
  9. Point(xAxis) → I
  10. Point(xAxis) → J
  11. Semicircle(A, J) → c
  12. Midpoint(A, J) → K
  13. OrthogonalLine(K, xAxis) → f
  14. Mirror(H, J) → H'
  15. Mirror(J, H') → J'
  16. Mirror(H', J') → H''
  17. Mirror(J', H'') → J''
  18. Semicircle(B, J'') → d
  19. Midpoint(B, J'') → L
  20. OrthogonalLine(L, xAxis) → g
  21. Intersect(d, g, 1) → M
  22. Segment(L, M) → h