unsolved_puzzles
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| unsolved_puzzles [2019/09/25 10:01] – [Shortest-path-preserving rounding of weights in a graph] administrator | unsolved_puzzles [2023/09/05 11:23] (current) – [A lower bound on the dilation of plane-filling curves] administrator | ||
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| ===== A lower bound on the dilation of plane-filling curves ===== | ===== A lower bound on the dilation of plane-filling curves ===== | ||
| - | Let τ: [0,1] → //T// be a continuous surjection to a compact set //T// in the plane such that for any //a// ≤ //b// ∈ [0,1], the union of τ(//t//) over all //t// ∈ [// | + | Let τ: [0,1] → //T// be a continuous surjection to a compact set //T// in the plane such that for any //a// ≤ //b// ∈ [0,1], the union of τ(//t//) over all //t// ∈ [// |
| In other words, τ is a measure-preserving plane-filling curve. The dilation of the curve is the maximum, over all //a// < //b// ∈ [0,1], of ||τ(// | In other words, τ is a measure-preserving plane-filling curve. The dilation of the curve is the maximum, over all //a// < //b// ∈ [0,1], of ||τ(// | ||
unsolved_puzzles.txt · Last modified: 2023/09/05 11:23 by administrator
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