五次方程的根
11 2025-11-29 08:45
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Use my code, 2SWAPYT20, for a 20% discount on your first purchase of a Lovable Pro plan before December 26! Click here to automatically apply the discount at checkout: https://lovable.link/2swapyt Check out the interactive polynomial solutions demo here: https://2swap.github.io/LittlewoodFra... If you liked this, please support me on Patreon! 
/ 2swap You can support the musician, 6884, on Kofi: https://ko-fi.com/iam6884 Check out his music here! https://6884.bandcamp.com/ This video was animated using SwapTube! https://github.com/2swap/swaptube Join our discord server here, where we talk about math, CS, puzzles, etc! 
/ discord === Errata === Found by @samuelwaid: at 12:26 I said "we define i as being the [square root of -1]" but the actual convention is to define i as being an element such that i^2 = -1. As mentioned in the video, there are various valid definitions of the square root function, and for some of them, the "definition" of i mentioned in the video would not be respected. Found by @fumeal: at 11:37 I said that the set of operators on screen were continuous and single valued. However the division operator is not continuous at z=0. === Sources and References === This video was primarily inspired by a paper by Leo Goldmakher. It covers the main proof of this video in a more academic fashion. https://web.williams.edu/Mathematics/... The proof itself is by Vladimir Arnold: https://en.wikipedia.org/wiki/Vladimi... While I was interested in Leo's paper, I saw this post about fractals of polynomial solutions. The images were somewhat low-resolution, which inspired me to make my own in conjunction with the topic of the video. https://les-mathematiques.net/vanilla... / https://web.archive.org/web/202405301... This excellent talk by Andrej Bauer was recommended to me while making my video. It goes much deeper into detail about the fractals of roots seen here. His talk prompted the comment about the dragon curve in this video. 
• 'Zeros' by Andrej Bauer Here are some other resources about the Abel-Ruffini theorem which I found along the way that helped with my own understanding: This tool helped me enormously in animating the paths of my roots and coefficients through complex space. Note the box that shows the roots of the determinant- compare to the "poles" in my animation: https://duetosymmetry.com/tool/polyno... Another easy-to-read paper covering this proof: https://arxiv.org/abs/2011.05162 Two more youtube videos covering this proof: • Why There's 'No' Quintic Formula (proof wi... • Short proof of Abel's theorem that 5th deg...
/ 2swap You can support the musician, 6884, on Kofi: https://ko-fi.com/iam6884 Check out his music here! https://6884.bandcamp.com/ This video was animated using SwapTube! https://github.com/2swap/swaptube Join our discord server here, where we talk about math, CS, puzzles, etc! / discord === Errata === Found by @samuelwaid: at 12:26 I said "we define i as being the [square root of -1]" but the actual convention is to define i as being an element such that i^2 = -1. As mentioned in the video, there are various valid definitions of the square root function, and for some of them, the "definition" of i mentioned in the video would not be respected. Found by @fumeal: at 11:37 I said that the set of operators on screen were continuous and single valued. However the division operator is not continuous at z=0. === Sources and References === This video was primarily inspired by a paper by Leo Goldmakher. It covers the main proof of this video in a more academic fashion. https://web.williams.edu/Mathematics/... The proof itself is by Vladimir Arnold: https://en.wikipedia.org/wiki/Vladimi... While I was interested in Leo's paper, I saw this post about fractals of polynomial solutions. The images were somewhat low-resolution, which inspired me to make my own in conjunction with the topic of the video. https://les-mathematiques.net/vanilla... / https://web.archive.org/web/202405301... This excellent talk by Andrej Bauer was recommended to me while making my video. It goes much deeper into detail about the fractals of roots seen here. His talk prompted the comment about the dragon curve in this video. • 'Zeros' by Andrej Bauer Here are some other resources about the Abel-Ruffini theorem which I found along the way that helped with my own understanding: This tool helped me enormously in animating the paths of my roots and coefficients through complex space. Note the box that shows the roots of the determinant- compare to the "poles" in my animation: https://duetosymmetry.com/tool/polyno... Another easy-to-read paper covering this proof: https://arxiv.org/abs/2011.05162 Two more youtube videos covering this proof: • Why There's 'No' Quintic Formula (proof wi... • Short proof of Abel's theorem that 5th deg... 分类
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