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.

Thanks!

#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:

[yb]

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

[wyattstevens]

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

[aschetos]

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

[sohammaheshwari]

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

[armchair]

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

[ebgurif]

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

[avijitpramanik]

Visualising is the best way to understand math😊

Do you agree 👍

[raulsantamariadominguez]

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.

[KayneBanham]

Why did he say purple when it's blue

[monkeybrain]

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