Home
Random
Nearby
Log in
Settings
Donate
About Wikipedia
Disclaimers
Search
Template
:
AM GM inequality visual proof.svg
Template
Talk
Language
Watch
Edit
Proof without words
of the
AM–GM inequality
:
PR is the diameter of a circle centered on O; its radius AO is the
arithmetic mean
of
a
and
b
. Using the
geometric mean theorem
, triangle PGR's
altitude
GQ is the
geometric mean
. For any ratio
a
:
b
,
AO ≥ GQ.