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New Lower Bound of 4.5058 Established for Packing 17 Unit Squares
Key points
- New lower bound for s(17) is 4.5058.
- Previous lower bound was 4.4811, set recently by Sam Burns.
- Original lower bound was 4.4452, established by Trevor Green in 2000.
- The upper bound for s(17) remains 4.6756.
Improved Lower Bound for s(17)
A new lower bound for s(17), which represents the side length of the smallest square capable of enclosing 17 unit squares, has been determined to be 4.5058. This calculation refines previous findings and contributes to the ongoing research in square packing problems.
Context of Square Packing Problem
The problem of square packing involves finding the smallest square that can contain a given number of unit squares. For n=17, the upper bound for s(17) was established in 1998 by John Bidwell at 4.6756. The lower bound has been progressively refined over time.
Trevor Green set an initial lower bound of 4.4452 in 2000. More recently, Sam Burns proposed an improved lower bound of 4.4811, which is currently awaiting community review.
Methodology and Impact
The new lower bound of 4.5058 was achieved through improvements to an existing program and methodology. This result further narrows the range for the true value of s(17), which now stands between 4.5058 and 4.6756. Further technical details regarding the derivation of this new bound are expected in a subsequent publication.
✨ This summary was generated by AI from the outlets' reporting listed below. It is not independently verified and may contain errors — check the original sources. How BrevFeed works →
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Reporting from
A new lower bound for s(17), the side length of the smallest square that can enclose 17 unit squares, has been established at 4.5058. This improves upon a recent result of 4.4811 and the previous long-standing bound of 4.4452, narrowing the range for s(17).