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The most beautiful formula not enough people understand 61 perc 
Why Africa Is Building a Wall Across the Entire Continent 54 perc 
马知墨祭出太玄八卦图，水墨特效炸裂 #凡人修仙传 #国漫 #shorts #donghua #madebybilibili【加入会员专享最新集】 1 perc 
《时光代理人 第三季》第6话花絮：bahati学院难道都是超能力儿童？【加入会员享最新集】 4 perc 
这么会挑对手啊？天哭道友 #凡人修仙传 #国漫 #shorts #donghua #madebybilibili【加入会员专享最新集】 1 perc 
The Prisoner of Bogan 32 perc 
Amtrak's Subtle, Surprising Success 20 perc 
American Fiction (2023) 4K - "We's Lives in Da Ghetto" Book (1/12) | Movieclips 2 perc 
谷双蒲欲摧毁大阵核心，韩立使用乾蓝冰焰击杀！#国漫 #shorts #donghua #madebybilibili【加入会员专享最新集】 1 perc 
Tom the Detective 🕵️🔍 #TalkingTomShorts 1 perc 
《凡人修仙传》第190话花絮：谷双蒲亮明内奸身份，陆道友惨遭毒手？【加入会员专享最新集】 5 perc 
Тут Очень Глубоко! (Pratfall) 21 perc 
KONTRAST 3 perc 
Europe's Most Remote Island Village (400 people live here) 41 perc 
How Apple AirPods Work 19 perc 
How can you overcome writer’s block? 1 perc 
Hurricane vs. Tiny Houses 23 perc 
Blade Runner 11 perc 
Samsung S26 Ultra Hands on - What's ACTUALLY New? 15 perc 
Humanity’s Real Plan to Stop This Asteroid (Feat. Mark Rober) 22 perc 
Buying a 1 euro House in Italy - is it a scam? 42 perc 
What If I Fell Into A Black Hole? 20 perc 
I Promise you this is NOT Stupid 10 perc 
Gen Z is done with both political parties | America, Actually 35 perc 
How We Built The ISS 37 perc 
How Google broke the internet | The Gray Area 40 perc 
Psychedelics, mind control, radiation-eating: The secret superpowers of fungi - Max G. Levy 7 perc 
The Hardest Problem AI Ever Solved, with Google DeepMind CEO 66 perc 
Sam Altman Shows Me GPT 5... And What's Next 66 perc 
The Craziest Experiment Humans Have Ever Built 18 perc 
Plasma Globe is a ⚡Shocking⚡🔥Fire Hazard🔥 12 perc 
The Problems with China's Space Program 17 perc 
Why American Houses Are So Flimsy 15 perc 
The World’s Best Diet Doesn’t Make You Lose Weight 13 perc 
Crash Course Hosts Read Comments 2 perc 
TED-Ed's top 10 animations of 2022! #shorts 1 perc 
The Grid That Doubles the Strength of the Ground 19 perc 
How Nike Lost Its Way 19 perc 
The Insane Engineering of the P-38 Lightning 27 perc 
Is it Possible to Prepare for an Earthquake?: Crash Course Geology #15 13 perc 
Prohibition - OverSimplified 34 perc 
Will gas prices decide the midterms? | America, Actually 28 perc 
Why you can’t walk anywhere in the US 2 perc 
Election deniers on the ballot 2 perc 
How Deep is the DEEPEST Submarine? 1 perc 
The Surprisingly Large Carbon Footprint of Rice #science #scishow #rice #climatechange 1 perc 
Name That Infrastructure (Ep. 5) #shorts 1 perc 
What's Under Your Feet in New York City? 23 perc 
What happens when we coat a pingpong ball with metal? #tbt #hacksmith #makeitreal 2 perc 
An Engineer's Perspective on the Texas Floods 24 perc 
How Self Storage Consumed America 19 perc On the volumes of higher-dimensional spheres Explore the 3b1b virtual career fair: See https://3b1b.co/talent Become a supporter for early views of new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Thanks to UC Santa Cruz for letting me film there, and special thanks to Pedro Morales-Almazan for arranging everything. My video on Numberphile with a fun application of this problem: https://youtu.be/6_yU9eJ0NxA Timestamps: 0:00 - Introduction 1:01 - Random puzzle 6:16 - Outside the box 14:35 - Setting up the volume grid 21:14 - Why 4πr^2 25:21 - Archimedes in higher dimensions 36:17 - The general formula 40:40 - 1/2 factorial 44:58 - Why 5D spheres are the biggest 50:16 - Concentration at the surface 54:27 - A unit-free interpretation 57:50 - 3b1b Talent 59:13 - Explaining the intro animation ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://3b1b.co/faq#manim Music by Vincent Rubinetti. https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: https://3blue1brown.substack.com Twitter: https://twitter.com/3blue1brown Bluesky: https://bsky.app/profile/3blue1brown.com Instagram: https://www.instagram.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Facebook: https://www.facebook.com/3blue1brown Patreon: https://patreon.com/3blue1brown Website: https://www.3blue1brown.com
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