PreprintCC BY 4.0arXiv
Littlewood's mutually touching cylinders: the maximum is seven
Abstract
We give a computer-assisted proof that eight congruent infinite circular cylinders in ℝ3 cannot touch pairwise. Since seven such cylinders exist, the maximum number of congruent mutually touching infinite cylinders is seven. This answers a question of Littlewood from 1968.
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BibTeX
@misc{matic2026littlewoods,
title = {{Littlewood's mutually touching cylinders: the maximum is seven}},
author = {Ivan Matić and Radoš Radoičić and Andreas Spomer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26940},
eprint = {2610.26940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26940},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Littlewood's mutually touching cylinders: the maximum is seven
AU - Ivan Matić
AU - Radoš Radoičić
AU - Andreas Spomer
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.26940
UR - https://arxiv.org/abs/2610.26940
AB - We give a computer-assisted proof that eight congruent infinite circular cylinders in ℝ^3 cannot touch pairwise. Since seven such cylinders exist, the maximum number of congruent mutually touching infinite cylinders is seven. This answers a question of Littlewood from 1968.
ER -