File:AM GM inequality visual proof.svg
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Summary
| Description |
English: Proof without words of the inequality of arithmetic and geometric means, drawn by CMG Lee. PR is a diameter of a circle centred on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, right triangle PGR can be split into two similar triangles PQG and GQR; GQ / a = b / GQ, hence GQ = √(ab), the geometric mean. |
| Source | Own work |
| Author | Cmglee |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 01:44, 10 October 2020 | | 512 × 341 (2 KB) | Cmglee | {{Information |description ={{en|1=Proof without words of the inequality of arithmetic and geometric means, drawn by CMG Lee. PR is a diameter of a circle centred on O; its radius AO is the arithmetic mean of ''a'' and ''b''. Using the geometric mean theorem, right triangle PGR can be split into two similar triangles PQG and GQR; GQ / ''a'' = ''b'' / GQ, hence GQ = √(''ab''), the geometric mean.}} |date = |source ={{own}} |author =User:Cmglee }} [[Category... |
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