Sum of positive number and its reciprocal from two triangles

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.
To buy me a coffee, head over to www.buymeacoffee.com/VisualPr...
Thanks!
For a wider format and slightly longer version of this proof, see • x plus 1/x is greater ...
It turns out that this theorem is equivalent to the Arithmetic Mean-Geometric Mean inequality. The equivalence is implied by the fact that his video resembles a similar visual proof for the AM-GM inequality found here: • Visual Proof of AM-GM ...
This animation is based on a proof by Roger B. Nelsen from the December 1994 issue of Mathematics Magazine, page 374 (doi.org/10.2307/2690999).
#math​ #manim​ #visualproof​ #mathvideo​ #geometry #mathshorts​ #algebra #mtbos​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #proof​ #iteachmath #inequality #amgm #maths #mathematics #education
To learn more about animating with manim, check out:
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[@yb3604]

this channel is brilliant
when x=1, the whole shape becomes a 1x1 square, with the hypotenuses of the triangles coming together as the diagonal of said square

[@MathVisualProofs]

:)

[@wyattstevens8574]

When does equality hold based on the diagram? An isosceles right triangle, the case where x=1.

[@appel-seed_]

Math is cool

[@aschetos]

Equality holds When x = 1, because inverse of 1 is 1.

[@DanielPoupko]

Bro *really* likes this result

[@KayneBanham]

Why did he say purple when it's blue

[@armchair8258]

Cool! Another way : 1/2(x+1/x)>=sqrt(x times 1/x)=1

[@LordMarshyMan]

X=1

[@prince_bk]

1+1/1=2≥2

[@sohammaheshwari8487]

Yoooo I just learned this yesterday and the teacher said to memorize it and u showed me the proof thanks for your help ❤❤

[@MathVisualProofs]

Glad I could help!

[@ebgurif]

I get a feeling that you seem to really love the x + 1/x >= 2 proofs

[@MathVisualProofs]

Just had four to do. All done now. I do like that this fact is equivalent to AM-GM (two var) so same pics work :)

[@avijitpramanik5425]

Visualising is the best way to understand math😊
Do you agree 👍

[@raulsantamariadominguez7511]

The inequality holds that the sum of an integer and its reciprocal is equal or bigger than 2. The sum of the least integer, 1, plus its reciprocal, 1/1, is 2; when x=2, (reciprocal, 1/2) is 2.5, for 3 is 3.3 and so on.

[@raulsantamariadominguez7511]

The bigger the "x" is, the sum of "x" and its reciprocal is equal to (approaches) "x".

[@Program0101]

Litterly ❤

[@billymays972]

Fax

[@monkeybrain2]

I am watching this at 1:40 AM and no I didin't understand shit

[@anteconfig5391]

Could it be when x is greater than 1?

[@rumamoitra3822]

Yes

[@joeleonard1314]

What now?

[@sohyankeat2031]

Cmon dallas game 3 up yr game kyrie