order of six means

The of the six usual means of two positive numbers (a and b) is from the least to the greatest one

  1. 1.
  2. 2.
  3. 3.
  4. 4.
  5. 5.
  6. 6.

i. e.


The equality signs are valid iff  a=b.

Proof.  If  x2-y20  for nonnegative x and y,  then  xy.


23” and “34”: proven in  Heronian mean is between geometric and arithmetic mean



Title order of six means
Canonical name OrderOfSixMeans
Date of creation 2013-03-22 18:45:28
Last modified on 2013-03-22 18:45:28
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 4
Author pahio (2872)
Entry type Theorem
Classification msc 06A05
Classification msc 26B35
Classification msc 26D07
Related topic Mean3
Related topic ComparisonOfPythagoreanMeans
Related topic InequalityWithAbsoluteValues
Related topic LehmerMean