Sum of a Positive Number and its Reciprocal from Calculus
This is a short, animated visual proof demonstrating that sum of a positive real number and its reciprocal is always greater than or equal to 2.
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It turns out that this theorem is equivalent to the Arithmetic Mean-Geometric Mean inequality. The equivalence is implied by the following two proofs: • Visual Proof of AM-GM Inequality I
• x + 1/x is greater than or equal to 2...
And here are two alternate ways to prove this fact via the Pythagorean Theorem and triangle areas:
• x plus 1/x is greater than or equal t...
• x plus 1/x is greater than or equal t...
This animation is based on a proof by Roger B. Nelsen from the December 1994 issue of Mathematics Magazine, page 374 (https://doi.org/10.2307/2690999). You can find this here too: https://www.maa.org/sites/default/fil...
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