回复 3楼 nj_guy 的帖子 这个问题是有半个多世纪历史，但是根本不是什么“著名”问题。 研究过搬沙发问题的Dan Romik在他的文章Differential equations and exact solutions in the moving sofa problem https://arxiv.org/pdf/1606.08111 写道 In 1966, the mathematician Leo Moser asked [15] the following curious question, which came to be known as the moving sofa problem: What is the planar shape of maximal area that can be moved around a right-angled corner in a hallway of unit width? Fifty years later, the problem is still unsolved. Thanks to its whimsical nature and the surprising contrast between the ease of stating and explaining the problem and the apparent difficulty of solving it, it has been mentioned in several books [7, 8, 20, 23], has dedicated pages describing it on Wikipedia [1] and Wolfram MathWorld [22], and, especially in recent years, has been a popular topic for discussion online in math-themed blogs [5, 6, 11, 16, 19] and online communities [2, 3]. (As further illustrations of its popular appeal, the moving sofa problem is the first of three open problems mentioned on the back cover of Croft, Falconer and Guy’s book [7] on 148 unsolved problems in geometry, and is currently the third-highest-voted open problem from among a list of 99 “not especially famous, long-open problems which anyone can understand” compiled by participants of the online math research community MathOverflow [3].) 黑体字由我给出。从他的描述就能看出搬沙发问题不是什么太重要的问题。
回复 3楼 nj_guy 的帖子 这个问题是有半个多世纪历史，但是根本不是什么“著名”问题。 研究过搬沙发问题的Dan Romik在他的文章Differential equations and exact solutions in the moving sofa problem https://arxiv.org/pdf/1606.08111 写道 In 1966, the mathematician Leo Moser asked [15] the following curious question, which came to be known as the moving sofa problem: What is the planar shape of maximal area that can be moved around a right-angled corner in a hallway of unit width? Fifty years later, the problem is still unsolved. Thanks to its whimsical nature and the surprising contrast between the ease of stating and explaining the problem and the apparent difficulty of solving it, it has been mentioned in several books [7, 8, 20, 23], has dedicated pages describing it on Wikipedia [1] and Wolfram MathWorld [22], and, especially in recent years, has been a popular topic for discussion online in math-themed blogs [5, 6, 11, 16, 19] and online communities [2, 3]. (As further illustrations of its popular appeal, the moving sofa problem is the first of three open problems mentioned on the back cover of Croft, Falconer and Guy’s book [7] on 148 unsolved problems in geometry, and is currently the third-highest-voted open problem from among a list of 99 “not especially famous, long-open problems which anyone can understand” compiled by participants of the online math research community MathOverflow [3].) 黑体字由我给出。从他的描述就能看出搬沙发问题不是什么太重要的问题。 ecaeca 发表于 2024-12-21 12:46
目前看跟Fields奖差得太远。
为啥？这也是有半个世纪的著名open question。我没有 follow details， 只是看新闻，请展开说说为啥认为“差太远”？是手段太简单？
这个问题是有半个多世纪历史，但是根本不是什么“著名”问题。
研究过搬沙发问题的Dan Romik在他的文章Differential equations and exact solutions in the moving sofa problem https://arxiv.org/pdf/1606.08111 写道
In 1966, the mathematician Leo Moser asked [15] the following curious question, which came to be known as the moving sofa problem:
What is the planar shape of maximal area that can be moved around a right-angled corner in a hallway of unit width?
Fifty years later, the problem is still unsolved. Thanks to its whimsical nature and the surprising contrast between the ease of stating and explaining the problem and the apparent difficulty of solving it, it has been mentioned in several books [7, 8, 20, 23], has dedicated pages describing it on Wikipedia [1] and Wolfram MathWorld [22], and, especially in recent years, has been a popular topic for discussion online in math-themed blogs [5, 6, 11, 16, 19] and online communities [2, 3]. (As further illustrations of its popular appeal, the moving sofa problem is the first of three open problems mentioned on the back cover of Croft, Falconer and Guy’s book [7] on 148 unsolved problems in geometry, and is currently the third-highest-voted open problem from among a list of 99 “not especially famous, long-open problems which anyone can understand” compiled by participants of the online math research community MathOverflow [3].)
黑体字由我给出。从他的描述就能看出搬沙发问题不是什么太重要的问题。
Okey 可能对数学的发展没有太大的重要性，不在主干道上，但还是很“著名”的，随便找个略知数学的人，大概率知道这个问题。
这个跟那个一根棍子 反转 180 度， 可以扫过面积是零 那个 哪个更有名一点。
搬沙发问题在数学爱好者中有一定名气，因为比较容易理解也比较有趣，但是在数学研究人员里太不受关注了。比如去mathscinet搜一搜，题目含有sofa的数学论文总共只有8篇，虽然数学论文总体不太多，这个数量也太少了。比较一下，题目含有sphere packing的数学论文总共有480篇，含有optimal transport的有1008篇，这才是能得Fields奖的题目应有的关注度。
你说的是挂谷问题（Kakeya needle problem），好像比搬沙发问题有名一些。
https://www.ucdavis.edu/blog/solving-moving-sofa-problem