From f002dda83175991aa9882f5159c0e56a734bfbd9 Mon Sep 17 00:00:00 2001 From: Andrew Yoo <199436365+andrew-yoo@users.noreply.github.com> Date: Fri, 26 Jun 2026 14:07:20 -0400 Subject: [PATCH 1/2] Update 41a and 41b --- constants/41a.md | 2 +- constants/41b.md | 44 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 45 insertions(+), 1 deletion(-) create mode 100644 constants/41b.md diff --git a/constants/41a.md b/constants/41a.md index 2e7315a..0214c80 100644 --- a/constants/41a.md +++ b/constants/41a.md @@ -2,7 +2,7 @@ ## Description of constant -The moving sofa constant $C\_{41}=A$ is the maximum area of a connected, rigid planar shape that can maneuver through an L-shaped corridor of unit width. +The moving sofa constant $C\_{41a}=A$ is the maximum area of a connected, rigid planar shape that can maneuver through an L-shaped corridor of unit width. The corridor is formed by two semi-infinite strips of width 1 meeting at a right angle. The problem asks for the shape of the largest area (the "sofa") that can be moved from one end of the corridor to the other by a continuous rigid motion (translation and rotation). diff --git a/constants/41b.md b/constants/41b.md new file mode 100644 index 0000000..4e48d49 --- /dev/null +++ b/constants/41b.md @@ -0,0 +1,44 @@ +# Ambidextrous Moving Sofa Constant + +## Description of constant + +The ambidextrous moving sofa constant $C\_{41b}$ asks for the maximum area of a sofa, as defined in $C\_{41a}$ that can navigate both left and right corners inside a Z-shaped corridor of width 1, where the corners are sufficiently far apart. +That is, the shape of the largest area (the "sofa") that can be moved from one end of the corridor to the other by a continuous rigid motion (translation and rotation). +Trivially, $C\_{41a} \ge \_{41b}$ + +## Known upper bounds + +| Bound | Reference | Comments | +| ----- | --------- | -------- | +| $2 \sqrt{2}$ | [Hammersley1968] | Intended for $C\_{41a}$, but can be modified for $C\_{41b}$ | +| 2.2195 | [Baek2024] | Naive bound from $C\_{41a}$ | + +## Known lower bounds + +| Bound | Reference | Comments | +| ----- | --------- | -------- | +| 1.64495 | [Gibbs2014] | Numerical result | +| 1.64495521 | [Romik2016] | | + +## Additional comments +- [Wikipedia section](https://en.wikipedia.org/wiki/Moving_sofa_problem#Ambidextrous_sofa) +- Another question posed by Conway considers a T-shaped intersection. It is unknown whether the two problems are equivalent. + + +## References + +- [Baek2024] Baek, J. (2024). +Optimality of Gerver's Sofa. +[arXiv:2411.19826](https://arxiv.org/abs/2411.19826). + +- [Gibbs2014] Philip Gibbs (2014). +A Computational Study of Sofas and Cars. +[vixra:1411.0038v2](https://vixra.org/pdf/1411.0038v2.pdf). + +- [Hammersley1968] J. M. Hammersley (1968). +On the enfeeblement of mathematical skills by modern mathematics and by similar soft intellectual trash in schools and universities. Bulletin of the Institute of Mathematics and Its Applications. +4: 66–85. See Appendix IV, Problems, Problem 8, p. 84. + +- [Romik2016] Dan Romik (2016). +Differential equations and exact solutions in the moving sofa problem. +[arxiv:1606.08111](https://arxiv.org/abs/1606.08111). \ No newline at end of file From a3542ec1629d1d83333760d20bdc28961a92190d Mon Sep 17 00:00:00 2001 From: Andrew Yoo <199436365+andrew-yoo@users.noreply.github.com> Date: Fri, 26 Jun 2026 14:14:58 -0400 Subject: [PATCH 2/2] Update README --- README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index cfeef46..e85c4c6 100644 --- a/README.md +++ b/README.md @@ -73,7 +73,8 @@ Bounds for which the level of available verification is currently at minimal lev | [39](https://teorth.github.io/optimizationproblems/constants/39a.html) | Hadwiger covering / illumination number in $\mathbb{R}^3$ | 8 | 14 | | [40a](https://teorth.github.io/optimizationproblems/constants/40a.html) | Lehmer’s Mahler measure constant | 1 | 1.176280... | | [40b](https://teorth.github.io/optimizationproblems/constants/40b.html) | Asymptotic Dobrowolski constant for Lehmer’s problem | $9/4$ | $\infty$ | -| [41](https://teorth.github.io/optimizationproblems/constants/41a.html) | Moving sofa constant | 2.2195 | 2.37 (2.2195*)| +| [41a](https://teorth.github.io/optimizationproblems/constants/41a.html) | Moving sofa constant | 2.2195 | 2.37 (2.2195*)| +| [41b](https://teorth.github.io/optimizationproblems/constants/41a.html) | Ambidextrous moving sofa constant | 1.64495521 | 2.2195 | | [42](https://teorth.github.io/optimizationproblems/constants/42a.html) | Turan's pure power sum constant | 0.5 | 0.69368 | | [43](https://teorth.github.io/optimizationproblems/constants/43a.html) | Gilbert-Pollak conjecture (Steiner ratio) | 0.8559 | 0.86602540378 | | [44](https://teorth.github.io/optimizationproblems/constants/44a.html) | Maximal number of relevant variables in degree-$d$ Boolean functions | 1.5 | 4.394 |