Same perimeter, different areas: Which is the largest? The Isoperimetric Problem
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- เผยแพร่เมื่อ 7 ก.พ. 2025
- 🌟 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.
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!"
Your words were clear and your proofs were amazing. I really enjoy to watch this!
This is so RICH of a video! Chapeau bas!
Thank you! We appreciate that
Excellent work! It's fantastic to see Algerian content utilizing manim on TH-cam.
Just a suggestion: you may want to consider improving the sound recording quality.
Thank you sir for the advice !
Finally a video with the perfect speed and rigor level
So hyped to watch more of it
Simply astonishing !
Thank you!
Great video. Looking forward to more.
If you have at least an understanding of the language used in math and the concepts they represent, dude really gave an entire introductory course to shape theory. Hell yeah.
Keep up the good work
Thank you sir !
Good job, team ❤❤❤❤
Thank you sir !
Very nice content!
4:09 There's also the case r = omega (sorry, no Greek letters on my phone), signifying that the curve is real-analytic, i.e. its power series converges to itself. There exist infinitely-differentiable functions that are nowhere analytic.
Underrated video.
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.
Hilbert curve?
Never mind, it's not simple.
@@tomkerruish2982 Hilbert curves have nothing to do with this. I said compact, not dense. Compact, as a subset of R^2, just means closed and bounded. More generally, it means a topological space whose topology can be generated from a finite set and thus every open cover has a finite subcover.
@newwaveinfantry8362 The Hilbert curve is continuous, and thus maps compact sets to compact sets. However, it is clearly not rectifiable.
Great video!
So nice!
very good video
Thanks for the visit
Nice video. Visuals are good, but there are some issues with audio. Sometimes it's good, sometimes it's bad, overall, inconsistent
Ah yes, Mr. Fence and Mr. Field, thanks Kjartan Poskitt!
Can you share video code??
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?
Hello, we are happy that our video has spiked you curiosity!
I assume you're familiar with general topology and you have taken a real analysis course and an affine geometry course. A good book to start with is "Functions of several variables" by Martin Moskowitz and Fotios Paliogiannis which will provide you with the necessary foundations and preleminaries to move onto the book: "Curves and Surfaces" by Sebastian Montiel and Antonio Ros, it not only contains the content of this video (and much more) but also serves as a great introduction to differential geometry.
@MathVerseAnimated ah okay nice. Thank you!
Circle.
Break a leg guys 🩵😍
Thank you !
@@MathVerseAnimatedwhy is she telling you that?
A suggestion... Include background music and intro
Thank you for the suggestion!
Please, no background music, it is at best barely tolerable and invariably distracting.
When next video ??
We plan to post a new video this week about Catalan numbers! Be tuned!
@@MathVerseAnimated we will see :)
Why you skipped area integral proof?
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).
@@MathVerseAnimated yeah, it's not obvious at all how this integral relates to the area
why is the "proof" of arclength not a proof
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.
hi
Yeah, areas are weird.
audio sucks
Try not to spit in the mic
Thank you, we will be more mindful new time!
@@MathVerseAnimatedYou might want to install a pop filter...
mics should be at least 2 feet from your mouth better 3 feet!!
Try to be more polite next time... you are watching for free, remember.
@@عمرأبوستة-ح1ك he was spitting in the mic...its not an AMSR pervo channel...
The mic kills the video