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Arithmetic and Geometric Mean Inequality

Arithmetic and Geometric Mean Inequality
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2016-03-25 07:57
Inequality
This example demonstrates the inequality between arithmetic and geometric means. Key mathematical concepts include arithmetic and geometric means. Using GeoGebra commands such as Circle, Segment, Intersect, Point, and Polygon, the relationship between the two means is visually constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle((0, 0), (a + b) / 2) → c
  2. Segment(((-((a + b) / 2)), 0), ((-((a + b) / 2)) + a, 0)) → d
  3. Segment(((a + b) / 2 - b, 0), ((a + b) / 2, 0)) → e
  4. Segment(((-((a + b) / 2)) + a, 0), ((-((a + b) / 2)) + a, sqrt((a * b)))) → GM
  5. Intersect(c, d, 1) → A
  6. Intersect(c, GM, 1) → B
  7. Segment(A, B) → f
  8. Intersect(c, e, 1) → C
  9. Segment(B, C) → g
  10. Point(d) → D
  11. Polygon(A, B, D) → poly1, d_1, a_1, b_1
  12. Polygon(B, D, C) → poly2, c_1, b_2, d_2
  13. Segment((0, 0), (0, (a + b) / 2)) → AM
  14. Polygon(((-((a + b) / 2)) + a, 0), ((-((a + b) / 2)) + a, GM), ((-((a + b) / 2)) + a + GM, GM), ((-((a + b) / 2)) + a + GM, 0)) → poly3, i, j, k, l