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The most beautiful formula not enough people understand 61 min 
与秦牧再度擦肩时，世间已无班公措！#牧神记 #国漫 #shorts #donghua #madebybilibili 【加入会员专享最新集】 1 min 
《百日成王》第22话：还好有你！黄主管【奇幻 | 战斗 | 搞笑 | Made By Bilibili】 12 min 
PAW Patrol crosses lava while riding dinosaurs! 🦖🔥 1 min 
《牧神记》第98话：杀新皇【玄幻 | 修仙 | 小说改 | Made By Bilibili】 21 min 
《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 min 
Karen Gillan's Deadly Dance Fight | Jumanji: Welcome to the Jungle 5 min 
What are tariffs, and how do they work? 6 min 
Psychedelics, mind control, radiation-eating: The secret superpowers of fungi - Max G. Levy 7 min 
There’s something wrong with Hallmark’s youtube channel 19 min 
《时光代理人 第三季》第5话花絮：vein和刘枭过去因何结识？【加入会员享最新集】 4 min 
Digging A SECRET GARAGE Part 2 22 min 
Гигантский Коп Следит За Тобой 👀 (Militsioner) 16 min 
The Gaming Market is Starting to Break. 23 min 
I bought the most CURSED TECH on the internet ft. KSI 25 min 
That's Why We Believe 4 min 
Reading StarCloud’s Whitepaper So You Don’t Have To 22 min 
BYE 3 min 
iOS 27 Hands-On: Top 5 New Features! 16 min 
Последний Танец 🕺 (ARC Raiders) 22 min 
Держись в тени, иначе сгоришь!🔥 | Обновление в PEAK 13 min 
The fastest way to board a plane, according to mathematics - Rachel Yang 6 min 
Sony Just Brought Super Zoom Cameras Back From the Dead! (RX10V) 1 min 
Bankrupt - iRobot (Roomba Vacuum) 20 min 
Scientists Found A Better Language For AI Agents 7 min 
Living by the Electric Power Lines/Centers 13 min 
What should security leaders do with AI? They don’t know. 30 min 
Which of these is the best idea? 🤷♂️ #batmobile #batman #engineering 1 min 
1000 feet of wireless range on a mic this small 🤯 1 min 
The missing ingredient in how we learn 6 min 
The Wildest Take-Off of My Life 30 min 
This substance could revolutionize human waste 10 min 
We’ve just launched *five* new channels! #shorts 1 min 
Have you HEARD this?? 2 min 
Trust the process #shorts 1 min 
Turns out building dry stone walls is difficult 25 min 
What’s your best guess? #shorts 1 min 
How Scientists Build Consensus: Crash Course Scientific Thinking #5 11 min 
These Rocks Are Older Than the Sun 13 min 
What your nipple shape says about you 5 min 
How Water Shapes the Land: Crash Course Geology #9 10 min 
Magnets+Skateboard=Hoverboard 2 min 
Vegetarian Diets Are... Hot #shorts #science #SciShow 1 min 
The hinge for 1/4Ton DOOR 1 min 
The Hidden Engineering of Runways 19 min 
Every Pickup needs this!! 1 min 
18 GENIUS Workshop TIPS (that actually work) 13 min 
This is NUTS 1 min 
I Thought this would be Safe! 17 min 
IF James Bond lived in a 3 bedroom house 1 min 
NASA's Plutonium Problem 2 min 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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