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Geometric Proof of Arithmetic Mean-Geometric Mean Inequality for Two Variables

Geometric Proof of Arithmetic Mean-Geometric Mean Inequality for Two Variables
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2016-10-03 13:50
FunctionInequalityGeometric Construction
This example demonstrates the arithmetic mean-geometric mean inequality for two variables through a geometric approach. Key mathematical concepts include arithmetic mean, geometric mean, and similarity transformation. It utilizes commands such as Intersect, Point, Polygon, Segment, Line, OrthogonalLine, and Vector in GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, C, D) → poly1, a, b, c, d
  4. Segment(C, E) → f
  5. Segment(A, F) → g
  6. Line(C, A) → h
  7. OrthogonalLine(F, g) → i
  8. OrthogonalLine(F, g) → j
  9. Intersect(h, j) → H
  10. Vector(A, C) → v_4
  11. Polygon(I, A, F) → poly2, f_1, i_1, a_1
  12. Polygon(G, A, K) → poly3, k, g_1, a_2
  13. Segment(C, I) → l
  14. Segment(C, K) → m
  15. Vector(A, G) → v_5
  16. Polygon(L, A, F, M) → poly4, l_1, a_3, f_2, m_1