Same perimeter, different areas: Which is the largest? The Isoperimetric Problem

🌟 Welcome to MathVerse Animated! 🌟
Dive deep into the heart of mathematics with our inaugural video: "The Isoperimetric Problem."
🔍 Join us on a captivating exploration of one of the most intriguing puzzles in geometry and calculus. From the ancient mathematicians of Greece to the modern minds of today, this video unveils the secrets behind shapes and their perimeters.
💡 Discover the origins of the Isoperimetric Problem and its significance in mathematical history. Unravel the mysteries surrounding optimal shapes and their boundaries, as we delve into the quest for maximizing area while minimizing perimeter.
🎥 Through engaging visuals and clear explanations, we'll guide you through the various approaches and solutions proposed by mathematicians over the centuries. Witness the beauty and elegance of mathematical reasoning as we unravel this timeless enigma.
🚀 Whether you're a seasoned mathematician, a curious learner, or simply fascinated by the wonders of the universe, this video promises to ignite your imagination and expand your understanding of the world around us.

[@benhur2806]

0:17 - Simple! Wrap the fence around yourself as tightly as possible, and shout "I define my current location to be outside of the enclosed area!"

[@ydjemmada]

Excellent work! It's fantastic to see Algerian content utilizing manim on KZbin. Just a suggestion: you may want to consider improving the sound recording quality.

[@MathVerseAnimated]

Thank you sir for the advice !

[@jaafars.mahdawi6911]

This is so RICH of a video! Chapeau bas!

[@MathVerseAnimated]

Thank you! We appreciate that

[@leobro2666]

Simply astonishing !

[@MathVerseAnimated]

Thank you!

[@newwaveinfantry8362]

Underrated video.

[@ShivacuuM]

Finally a video with the perfect speed and rigor level So hyped to watch more of it

[@aminezemirni]

Good job, team ❤❤❤❤

[@MathVerseAnimated]

Thank you sir !

[@PictooMath]

Your words were clear and your proofs were amazing. I really enjoy to watch this!

[@rezkichemlal4998]

Keep up the good work

[@MathVerseAnimated]

Thank you sir !

[@newwaveinfantry8362]

8:30 - I don't think you need this. Gamma is continuous and [a,b] is compact. Thus gamma([a,b]) is compact in R^2. Thus it is bounded, so it is rectifiable.

[@lexkoal8657]

Nice video. Visuals are good, but there are some issues with audio. Sometimes it's good, sometimes it's bad, overall, inconsistent

[@konstantin7596]

So nice!

[@taylorsmiles4143]

Great video. Looking forward to more.

[@rujon288]

very good video

[@MathVerseAnimated]

Thanks for the visit

[@AndrewBalm]

Very nice content!

[@DanDart]

Ah yes, Mr. Fence and Mr. Field, thanks Kjartan Poskitt!

[@John-pp2jr]

Circle.

[@SarahAliradi]

Break a leg guys 🩵😍

[@MathVerseAnimated]

Thank you !

[@spazmoidectomorf6209]

Do you learn this im differential geometry? I really like this stuf and the calculus of variations but i dont know where to start What books would you recommend?

[@pandavroomvroom]

why is the "proof" of arclength not a proof

[@MathVerseAnimated]

Well, "The sum becomes an integral and Δsomething becomes d something" is not really a mathematical sentence. If you want to make it into a proof, you have to use something like Riemann sums or similar to show that the sum converges to the integral.

[@ucngominh3354]

hi

[@gleleylo]

Why you skipped area integral proof?

[@MathVerseAnimated]

I'm not sure which one you're referring to, but if it's the first one, it doesn't need a proof because it's a definition :) if you mean seeing intuitively that it gives the area, we thought it was simple to see how to apply the same process as the one for the arc length (it later turned out this wasn't the case, and an explanation was warranted).

[@gleleylo]

@@MathVerseAnimated yeah, it's not obvious at all how this integral relates to the area

[@notu483]

Try not to spit in the mic

[@MathVerseAnimated]

Thank you, we will be more mindful new time!

[@benhur2806]

​@@MathVerseAnimatedYou might want to install a pop filter...

[@lunam7249]

mics should be at least 2 feet from your mouth better 3 feet!!

[@user-oc4gu9kb3p]

Try to be more polite next time... you are watching for free, remember.

[@lunam7249]

@@user-oc4gu9kb3p he was spitting in the mic...its not an AMSR pervo channel...