Unverified80% confidenceFactTime unknown
平面单位距离问题与Erdős-Szemerédi猜想、Erdős距离问题并列为组合几何三大经典难题
1
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80%
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Long-term
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5/31/2026
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UnverifiedErdős单位距离问题（Unit Distance Problem）问的是在平面上放置n个点，最多能有多少对点之间的距离恰好为179% similarUnverified几何内核最棘手的问题是数值鲁棒性，浮点误差在布尔运算中可能产生退化边或非流形拓扑66% similarUnverifiedBrass, Moser, and Pach described the unit distance problem in 'Research Problems in Discrete Geometry' as perhaps 'the most well-known and easily stated problem in combinatorial geometry.'61% similarUnverifiedThe Johnson-Lindenstrauss lemma guarantees that for any ε∈(0,1), as long as the target dimension k≥O(log(n)/ε²), there exists a mapping from high dimensions to k dimensions that preserves all pairwise distances within a factor of (1±ε).55% similarUnverifiedErdős conjectured that the upper bound of U(N) is N^(1+o(1)), where o(1) tends to 0 as N grows.54% similar
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