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, $C_{41a} \ge C_{41b}$
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
- Another question posed by Conway considers a T-shaped intersection. It is unknown whether the two problems are equivalent.
References
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[Baek2024] Baek, J. (2024). Optimality of Gerver’s Sofa. arXiv:2411.19826.
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[Gibbs2014] Philip Gibbs (2014). A Computational Study of Sofas and Cars. vixra:1411.0038v2.
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[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.
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[Romik2016] Dan Romik (2016). Differential equations and exact solutions in the moving sofa problem. arxiv:1606.08111.