Sum of a Positive Number and its Reciprocal from Calculus

Опубликовано: 06 Июнь 2024
на канале: Mathematical Visual Proofs
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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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To learn more about animating with manim, check out:
https://manim.community


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