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Solving problems by adding a dimension Solving problems by adding a dimension 30 min 2 LATE 2 LATE 2 min Новогодняя нарезка (Лучшее за 2025) Новогодняя нарезка (Лучшее за 2025) 82 min Blinded By A Rollercoaster: The Problem With Dragon Challenge | Fascinating Horror Blinded By A Rollercoaster: The Problem With Dragon Challenge | Fascinating Horror 10 min Я загрузил ИИ в Скайрим... и вот чот вышло 🤣 Я загрузил ИИ в Скайрим... и вот чот вышло 🤣 23 min Movies for Game Consoles - Scott The Woz Movies for Game Consoles - Scott The Woz 34 min Framework 13 Pro: The Modular Laptop is Real! Framework 13 Pro: The Modular Laptop is Real! 13 min iPhone 18 Pro/Duo Impressions: Mogged iPhone 18 Pro/Duo Impressions: Mogged 18 min Abandoned - Stitch's Great Escape Abandoned - Stitch's Great Escape 25 min Я загрузил ИИ в Скайрим… и создал чудовище 😈 Я загрузил ИИ в Скайрим… и создал чудовище 😈 26 min History's Worst Elevator Accident: Vaal Reefs | Fascinating Horror History's Worst Elevator Accident: Vaal Reefs | Fascinating Horror 10 min I Pranked A Celebrity Movie Premiere I Pranked A Celebrity Movie Premiere 31 min The Steam-Cooled STEAM Machine The Steam-Cooled STEAM Machine 26 min Luna Pro 4K Vertical Video Is a HUGE Upgrade! Luna Pro 4K Vertical Video Is a HUGE Upgrade! 1 min Stop Waking Up at 3AM! How to Fall Back Asleep FAST Stop Waking Up at 3AM! How to Fall Back Asleep FAST 2 min Mall versus Home Electrocution (Updated) Mall versus Home Electrocution (Updated) 14 min Who Is Logan?! (Marvel's Wolverine) Who Is Logan?! (Marvel's Wolverine) 145 min How to attack (and defend) a medieval castle - Connor C. Wilson How to attack (and defend) a medieval castle - Connor C. Wilson 6 min IBM’s cloud collab, Meta’s Muse Glimmer & OpenAI’s upcoming Astra model IBM’s cloud collab, Meta’s Muse Glimmer & OpenAI’s upcoming Astra model 37 min The Sketchiness in GREECE The Sketchiness in GREECE 26 min COUPLE OR BEST FRIENDS? Ft BETA SQUAD COUPLE OR BEST FRIENDS? Ft BETA SQUAD 24 min this makes video editing So SiMPLE! this makes video editing So SiMPLE! 1 min How to Use YouTube Studio in 2026! (Complete Guide) How to Use YouTube Studio in 2026! (Complete Guide) 19 min BREAKING: YouTube Just Changed Monetization BREAKING: YouTube Just Changed Monetization 20 min Stop Expecting AI Perfection ❌ Stop Expecting AI Perfection ❌ 1 min What are tariffs, and how do they work? What are tariffs, and how do they work? 6 min Journey to EPCOT Center: A Symphonic History Journey to EPCOT Center: A Symphonic History 70 min I Tested 21 Vlogging Cameras in 2026! (so you don't have to) I Tested 21 Vlogging Cameras in 2026! (so you don't have to) 32 min They Call It A "Drowning Machine" | Fascinating Horror Shorts They Call It A "Drowning Machine" | Fascinating Horror Shorts 1 min NVIDIA's Open Source Strategy🤖 NVIDIA's Open Source Strategy🤖 1 min DefunctTV: The History of Where in the World is Carmen Sandiego? DefunctTV: The History of Where in the World is Carmen Sandiego? 29 min World's LARGEST headphones! World's LARGEST headphones! 1 min PARADISE LOST PARADISE LOST 3 min Rain Rain 3 min $10,000 Power Washer! $10,000 Power Washer! 1 min This GPU can be Hacked to Unlock Secret Memory This GPU can be Hacked to Unlock Secret Memory 20 min These people walk towards mining disasters. These people walk towards mining disasters. 22 min (VR) Я ❤️ Работу | Часть 2 (Job Simulator) (VR) Я ❤️ Работу | Часть 2 (Job Simulator) 17 min The Hunt for Xesh The Hunt for Xesh 34 min Get 4 Tech Acronyms Win! Get 4 Tech Acronyms Win! 1 min The Gaming Market is Starting to Break. The Gaming Market is Starting to Break. 23 min Psychedelics, mind control, radiation-eating: The secret superpowers of fungi - Max G. Levy Psychedelics, mind control, radiation-eating: The secret superpowers of fungi - Max G. Levy 7 min DLSS 5.0 is out... kinda. DLSS 5.0 is out... kinda. 1 min 30 Day Body Transformation 30 Day Body Transformation 2 min We Rebranded Linus Media Group to... We Rebranded Linus Media Group to... 13 min DLSS 5 is NOT What We Expected DLSS 5 is NOT What We Expected 19 min ONE OF US ONE OF US 3 min I helped break a 142-year-old bell, and that's okay. I helped break a 142-year-old bell, and that's okay. 33 min iPhone Duo Hands On! iPhone Duo Hands On! 2 min Can a PS5 cook an egg? Can a PS5 cook an egg? 1 min How does the space station never run out of oxygen? - Alvaro Romero-Calvo and Theo St Francis How does the space station never run out of oxygen? - Alvaro Romero-Calvo and Theo St Francis 7 min

Solving problems by adding a dimension

2024 30 min

Five geometry puzzles solved by a clever shift in perspective. Bonus video with extra puzzles: https://www.patreon.com/posts/115570453 The artwork at the end is by Kurt Bruns Thanks to Daniel Kim for sharing the first two puzzles with me. He mentioned the earliest reference he knows for the tile puzzles is David and Tomei's AMM article titled "The problem of Calissons." The idea to include the tetrahedron volume example was based on a conversation with Po Shen Lo about these puzzles, during which he mentioned the case of one dimension lower. I received the cone correction to the proof of Monge's theorem from Akos Zahorsky via email. Also, the Bulgarian team leader, Velian Velikov, brought up the same argument and just shot me a message saying, "I came across it in a book I found online titled 'Mathematical Puzzles' by Peter Winkler. There, it is attributed to Nathan Bowler" I referenced quaternions at the end, and if you're curious to learn more, here are a few options. This is a nice talk targeted at game developers: https://youtu.be/en2QcehKJd8 This video walks through concretely what the computation is for using quaternions to compute 3d rotations: https://youtu.be/-zsnHbQyRnc My own video on the topic is mainly focused on understanding what they do up in four dimensions, which is not strictly necessary for using them, but for math nerds like me may be satisfying: https://youtu.be/d4EgbgTm0Bg Also, one of the coolest projects I've ever done was a collaboration with Ben Eater to make interactive videos based on that topic: https://eater.net/quaternions Timestamps - 0:00 - Intro - 0:32 - Twirling tiles - 6:45 - Tarski Plank Problem - 10:24 - Monge’s Theorem - 17:26 - 3D Volume, 4D answer - 18:51 - The hypercube stack - 25:52 - The sadness of higher dimensions SEV#3: https://youtu.be/vXBtyYvMx24 ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://3b1b.co/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ All code for specific videos is visible here: https://github.com/3b1b/videos/ The music is by Vincent Rubinetti. https://www.vincentrubinetti.com 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 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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