Understanding the Formula for Area of a Circle #shorts

#shorts Deriving the area of a circle formula by Geometric Proof

In this short, we derive the area of a circle formula using a geometric proof #VeritasiumContest

[fishiesgaming]

It always amazes me how ancient mathematicians found formulas like this in their time

[puzzLEGO]

This should be taught in schools, as soon as you start understanding why in maths you can more easily understand much harder concepts

[nandinimisra]

Many people in the comment section are explaining how there are much better explanation but when you are teaching this to a middle schooler you can't or should not use calculus or more difficult processes to explain it. This video is actually very helpful to teach a middle schooler how the formula works. It's very easy and helpful for them to memorize in this way.

[BakkuIa]

I haven't done geometry in six years, and this was amazing.
The formula was just a fact of the world in school, but to finally see the relation with other shapes is amazing.

[bozo]

Damn, visualizing it like this actually makes it a lot easier to comprehend, I kinda wish I was shown something like this in back in school

[TheFluke]

This short just made me realize that the formula for the area of a circle was never explained to me and my fellow schoolmates and we just accepted that it was what it was back when we were studying geometry. And even until college no one even bothered asking about it, or present it this way.

This has been an interesting bit of knowledge that would have been nice to have learned back when then.

[gaganbajaj]

What took me 2 days to understand back when I was in school, you explained within a minute. Well done

[The_Harsh_Truth]

Remember, Asking "WHY?" is something not everyone can do.

Teachers teach us and we just believe in it without any thought.
Asking Why is a big step towards learning something.

[trebelojaques]

This is just very well, animated. I hope schools show this video to visually illustrate how things go around. This could truly negate the reason of rot learning formulas. It takes time and the time constraints of one school year may not always suffice the 'visual derivation' of every formulae.

But definitely some, which are crucial, to our syllabi, could do wonders to our system. To ask 'why' more than 'what' to strike curiosity.

[gluten]

I remember getting shown this in school still remains one of the coolest things ever

[kaironcabaylo]

I'm so glad that my school actually taught me this because it really gives you an understanding and even if you can't understand what is going on, you can just simply learn the formula which is absolutely fine.

[fallen_piano]

What's crazy to me is that I was blown away by this same demonstration years ago without knowing Calculus. Now that I am older, I just realized how good this demonstrates the essence of Integral Calculus.

[plumith]

I swear to God what in the world I just watched this video in school today but it was a two or three minute video because it wasn’t sped up and it had a person explaining the more you cut a circle, the more flat the circle gets, like how Earth is a sphere and not flat but it appears flat to us because we’re focused on one extremely small spot of the sphere making it appear it’s flat

[Ziar]

I've just sorta accepted it but this makes it more intuitive, thanks!

[toastedwheat]

Simultaneously the easiest way to understand it and hardest to process it. Love it.

[antikovt]

I remember coming up with a nice visual reminder for myself. I would approximate the circle's area to 4 squares with a side length of r and then say that the area of a circle if roughly 3.14 of these squares, hence πr². Really helped me understand what π is and why it's the way it is. It's the amount of squares with side length r you need to fill the circle!

[calebwirt]

Very elegantly done- math is often too arbitrary for people who want to understand how and why something works rather than just accepting it, so breaking it down to something easily absorbed like this is awesome

[SAM]

This video literally taught me what my 10 years long school couldn't..◼️◼️

[dusundavarfreohr]

This is the best thing ever, literally
Like, I'm unironically glad to live in the age of internet rn

[michelelandolfi]

I have always found it easier to conceptualize it another way:
Find the area of a square which is one fourth of the circle (radius squared) then multiply it by the ratio between the area of a circle and a diameter sided square outside it (pi)