Math's Weirdest Paradox

Video Description

Take a sphere and disassemble it into finely many pieces. The Banach-Tarski Paradox guarantees, by means of a mathematical proof, that you can reassemble the pieces into 2 copies of the exact same, original sphere. How is this possible? Correction: 1:05 Sorry, should be (0, 2pi). See pinned comment for explanation _____ Join my Patreon community: https://www.patreon.com/abidebyreason Support the channel with a one-time donation: https://ko-fi.com/abidebyreason _____ Related Videos: Intro to Measure Theory: https://youtu.be/1BhSQiHTNbg What is the Measure of the Rationals vs Irrationals? https://youtu.be/1qbjjgesp-c Visualizing the Rationals: https://youtu.be/wE1iJkXs1Xg Intro to Topology: https://youtu.be/B-Y3-XpAdMU Intro to Group Theory: https://youtu.be/5qmsqwxrSLc _____ Animations created using Manim: https://www.manim.community/ Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k