Timeline for A question about the Kakeya problem
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2010 at 22:32 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
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| Jul 13, 2010 at 15:36 | answer | added | Andrey Rekalo | timeline score: 5 | |
| Jul 13, 2010 at 15:35 | history | edited | Willie Wong |
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| Jul 13, 2010 at 15:33 | comment | added | Willie Wong | Just a sketch: consider a motion of the needle (unit line segment), (assume) that it can be represented by a continuous and piece-wise $C^1$ curve in the space of Euclidean motions (translations + rotations). Restrict yourself to a $C^1$ portion such that the starting and ending angles are not the same (else there can be no total rotation). By the mean value theorem there exists a point on the path where the rate of change of the angle is non-zero. It should be straight-forward to check that the image of the needle in a neighborhood of that point contains a disk. | |
| Jul 13, 2010 at 15:33 | answer | added | Charles Matthews | timeline score: 0 | |
| Jul 13, 2010 at 15:16 | history | asked | Garabed Gulbenkian | CC BY-SA 2.5 |