Indicwiki: 1 revision imported from :alpha:Template:QM_AM_GM_HM_inequality_visual_proof.svg

2023-03-17T04:07:34Z

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alpha>Indicwiki: Created page with "Geometric [[proof without words that {{nowrap|''max'' (''a'',''b'')}} > {{nowrap|root mean squ..."

2023-02-03T12:15:19Z

Created page with "thumb|{{{1|230px}}}|Geometric [[proof without words that {{nowrap|''max'' (''a'',''b'')}} > {{nowrap|root mean squ..."

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[[File:QM_AM_GM_HM_inequality_visual_proof.svg|thumb|{{{1|230px}}}|Geometric [[proof without words]] that {{nowrap|''max'' (''a'',''b'')}} > {{nowrap|[[root mean square]] ('''RMS''')}} or {{nowrap|[[quadratic mean]] ('''QM''')}} > {{nowrap|[[arithmetic mean]] ('''AM''')}} > {{nowrap|[[geometric mean]] ('''GM''')}} > {{nowrap|[[harmonic mean]] ('''HM''')}} > {{nowrap|''min'' (''a'',''b'')}} of two distinct positive numbers ''a'' and ''b'' <ref>If AC = ''a'' and BC = ''b''. OC = '''AM''' of ''a'' and ''b'', and radius ''r'' = QO = OG. Using [[Pythagoras' theorem]], QC² = QO² + OC² &therefore; QC = √QO² + OC² = '''QM'''. Using Pythagoras' theorem, OC² = OG² + GC² &therefore; GC = √OC² − OG² = '''GM'''. Using [[similar triangles]], {{sfrac|HC|GC}} = {{sfrac|GC|OC}} &therefore; HC = {{sfrac|GC²|OC}} = '''HM'''.</ref>]]<noinclude>
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Template:QM AM GM HM inequality visual proof.svg - Revision history

Indicwiki: 1 revision imported from :alpha:Template:QM_AM_GM_HM_inequality_visual_proof.svg

alpha>Indicwiki: Created page with "Geometric [[proof without words that {{nowrap|''max'' (''a'',''b'')}} > {{nowrap|root mean squ..."