Timeline for Examples of theorems where numerical bounds on $\pi$ played a role
Current License: CC BY-SA 4.0
6 events
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| Jul 17 at 7:56 | comment | added | Dan Romik | (By the way, the figure in your answer shows Gerver's sofa, not Hammersley's sofa. They look pretty similar to each other though.) | |
| Jul 17 at 7:54 | comment | added | Dan Romik | So, one can make the correct statement that the numerical value of 𝜋 (together with the numerical value 2.2195 of Gerver's sofa) is why Hammersley's sofa is not the one with maximal area. But it is not why the problem is unsolved. The problem is unsolved simply because no one has been able to prove the conjectured maximality of Gerver's sofa, or to disprove it. This has nothing to do with my and Yoav Kallus's upper bound of 2.37, which is simply the best known bound at present. | |
| Jul 17 at 7:51 | comment | added | Dan Romik | The numerology in this answer is amusing, but the numerical value of 𝜋 is not why the problem is unsolved, and the fact that $\pi/2+2/\pi<2.37$ is not why Hammersley's sofa, which has area $\pi/2+2/\pi$, is not the solution to the moving sofa problem. The number 2.37 is only an upper bound, so its existence does not preclude the possibility that Hammersley's sofa might be the solution. On the other hand, Hammersley's sofa is indeed not the solution, but that's for a different reason than what you said - namely, because another shape, known as Gerver's sofa, has a larger area of around 2.2195. | |
| Jul 17 at 7:42 | history | edited | Dan Romik | CC BY-SA 4.0 |
corrected reference to paper by Kallus and Romik, incorrectly attributed only to Romik.
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| May 13 at 10:29 | history | edited | user479223 | CC BY-SA 4.0 |
added 302 characters in body
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| May 13 at 10:21 | history | answered | user479223 | CC BY-SA 4.0 |