The Banach-Tarski theorem says we can duplicate a solid, 3D ball. An extension of the theorem generalizes it to transforming any 3D shape into any new 3D shape of a new shape and size. It's a beautiful piece of math and demonstrates how infinity can have strange results.
Made for #some3 challenge - big thanks to Grant Sanderson (@3blue1brown )
Hopefully you at least learned... something? Even if you don't quite understand the paradox in full, I hope you at least learned a thing or two about infinity or about set theory.
Well, this was my first video. I’d love for you to tell me what I did well and what I should work on improving. I was definitely rushed for time for this video. I just didn’t realize how long animation can take. Because of this, I had to cut out several sections which would have made the proof more approachable and understandable, and the ending section is incomplete. Maybe I’ll make a follow-up, I don’t know… I do want to send massive thanks to Grant Sanderson, 3blue1brown, for organizing and hosting this Summer of Math Exposition. Though a tiny bit stressful because of my underestimated scope, this was fun and helpful for my brain. I might never have taken my hand at explaining stuff were it not for him so thanks!
TO LEARN MORE:
The book where I got a majority of this information is called The Pea and The Sun by Leonard M. Wapner. I could not recommend it enough if you're interested more in this topic. It assumes no background knowledge and explains everything.
Vsauce has made a good video on the topic here: • The Banach-Tarski Paradox
Everything in this video is my own: my own script, my own music and my own animations using blender.
Негізгі бет The Duplication Glitch in Math (Banach-Tarski Theorem)
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