File:AM_GM_inequality_visual_proof.svg
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Summary
DescriptionAM GM inequality visual proof.svg |
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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Date/Time | Thumbnail | Dimensions | User | Comment | |
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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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Short title | AM GM inequality visual proof |
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Image title | 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. |
Width | 100% |
Height | 100% |
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