Template:AM GM inequality visual proof.svg: Difference between revisions
Content deleted Content added
BostonMensa (talk | contribs) No edit summary |
+ 2 categories |
||
| Line 1: | Line 1: | ||
[[File:AM_GM_inequality_visual_proof.svg|thumb|{{{1|right}}}|[[Proof without words]] of the [[inequality of arithmetic and geometric means]]:<br style="margin-bottom:1ex;"/><math>PR</math> is the diameter of a circle centered on <math>O</math>; its radius <math>AO</math> is the [[arithmetic mean]] of <math>a</math> and <math>b</math>. {{nowrap|Using the [[geometric mean theorem]],}} {{nowrap|triangle <math>PGR</math>'s}} [[altitude_(triangle)|altitude]] <math>GQ</math> is the [[geometric mean]]. For any ratio {{nowrap|<math>a:b</math>,}} {{nowrap|<math>AO\ge GQ</math>.}}]]<noinclude> |
[[File:AM_GM_inequality_visual_proof.svg|thumb|{{{1|right}}}|[[Proof without words]] of the [[inequality of arithmetic and geometric means]]:<br style="margin-bottom:1ex;"/><math>PR</math> is the diameter of a circle centered on <math>O</math>; its radius <math>AO</math> is the [[arithmetic mean]] of <math>a</math> and <math>b</math>. {{nowrap|Using the [[geometric mean theorem]],}} {{nowrap|triangle <math>PGR</math>'s}} [[altitude_(triangle)|altitude]] <math>GQ</math> is the [[geometric mean]]. For any ratio {{nowrap|<math>a:b</math>,}} {{nowrap|<math>AO\ge GQ</math>.}}]]<noinclude> |
||
[[Category:Geometry templates]] |
|||
[[Category:Mathematics image insertion templates]] |
|||
{{Uncategorized|date=May 2023}} |
|||
</noinclude> |
</noinclude> |
||
Revision as of 00:54, 8 June 2023
is the diameter of a circle centered on ; its radius is the arithmetic mean of and . Using the geometric mean theorem, triangle 's altitude is the geometric mean. For any ratio , .
