AM-GM inequality visually

This is a short, animated visual proof of the arithmetic mean-geometric mean inequality using areas. This theorem states that the average of two positive numbers is greater than or equal to the square root of the product of the same two numbers (with equality only when the two numbers are the same). #math #amgminequality #area #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo

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Here are some other visual proof of the AMGM inequality (and others):

To learn more about animating with manim, check out:

[platosbeard]

Here's a challenge for ya – a visual proof of the general form. I'd prove this via forwards-backwards induction, which I don't think is that amenable to a visual proof, but there may be another way to do it 😀

[fsyi]

When a=b, the interior square doesn't exist. That can proof, a rectangle will reach its maximum area while varying within a fixed perimeter and its minimum perimeter while varying within a fixed area when it is a square

[kevina]

Kindof turned into a "side effects include" segment of drug advertisement towards the end lol

[viatori]

Was it just me or did you speed up a bit there at the end 😏

[kevinbihari]

When you thought the paper was longer and you are halfway the text with only 20% of the space left

[mathentic]

This is interesting, but my understanding from visual proof is one pretty clear and explanatory diagram. Not just making step by step using figures. For AMGM for example diameter and chord interpretation is pretty gooood

[machlipatnammachlipatnam]

This is also used in construction of traditional houses in southern India....mandava houses which we see in Tamil Nadu katnataka &andhra

[verma.shaurya]

Awesome... could you please do the same with HM as well?

[captinglow]

What do u use to make these amazing animations?

[countrypoint]

Though I didn't know this but found interesting

[sudarshanachakra.]

Middle square length would be b .Not b-a

[jeremycalnan-pmzd]

Like not one of my roommates ever paid rent to me ...so why should I pay rent for us or be ....the sole... response able party....Darby Keven and Bradly....why....

[ogmakefirefiregood]

I knew that intuitively. It's like knowing what a woman is. Duh.