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This open problem taught me what topology is

2024 28 นาที

The inscribed square/rectangle problem, solved using Möbius strips and Klein bottles. Playlist with more neat proofs: https://www.youtube.com/playlist?list=PLZHQObOWTQDPSKntUcMArGheySM4gL7wS Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. This argument was originally by Herbert Vaughan, appearing for examples in this issue of the Topology Proceedings. https://topology.nipissingu.ca/tp/reprints/v06/tp06107.pdf The on-screen argument for why all closed non-orientable surfaces must intersect themselves in 3d is a slight variation on one I heard from Dan Asimov. 2020 Paper by Greene and Lobb: https://arxiv.org/pdf/2005.09193 Nice Quanta article about this result: https://www.quantamagazine.org/new-geometric-perspective-cracks-old-problem-about-rectangles-20200625/ Timestamps: 0:00 - Inscribed squares 1:00 - Preface to the second edition 3:04 - The main surface 10:47 - The secret surface 16:45 - Klein bottles 22:38 - Why are squares harder? 25:10 - What is topology? ------------------ 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

ประเทศ

สหรัฐอเมริกา

ทำงานกับผู้สร้างคนนี้

แพ็กเกจที่เผยแพร่โดยผู้สร้างเบื้องหลังวิดีโอนี้

แพ็กเกจทั้งหมด

ผู้สร้างคนนี้ยังไม่ได้กำหนดอัตราของตน ส่งคำขอและเราจะส่งต่อไป — ราคาจะตกลงก่อนที่จะมีการเรียกเก็บใดๆ

การเข้าร่วมรายเดือน

ต่อเดือน

ที่นั่งที่เกิดขึ้นซ้ำในเนื้อหาของฉัน ผู้สมัครเข้าคิว — หรือจับฉลากเมื่อมีผู้สมัครมากกว่าช่อง — และปรากฏในวิดีโอเอง ในเครดิต หรือในคำอธิบาย

ราคาตามคำขอ

เข้าสู่ระบบเพื่อขอ

การวางตำแหน่งที่รับประกัน — วิดีโอใหม่

ครั้งเดียว

การปรากฏตัวที่รับประกันอย่างน้อย 10 วินาทีในวิดีโอถัดไปของฉัน ราคาขึ้นอยู่กับว่าการแทรกอยู่ตรงไหนของระยะเวลา

ราคาตามคำขอ

  • 1–3 นาทีแรก
  • กลางวิดีโอ
  • ท้ายวิดีโอ
เข้าสู่ระบบเพื่อขอ

การวางตำแหน่งที่รับประกัน — Short

ครั้งเดียว

การปรากฏตัวที่รับประกันอย่างน้อย 10 วินาทีใน Short ที่ตัดจากวิดีโอที่มีอยู่ของฉัน

ราคาตามคำขอ

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