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Timeline for One-step problems in geometry

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Dec 31, 2020 at 0:44 comment added Gjergji Zaimi @AntonPetrunin: It's in Matousek's book "Lectures on discrete geometry" (chapter 14). There I see that it is attributed to a paper by J. Arias-de-Reyna, K. Ball, R. Villa called "Concentration of the distance in finite dimensional normed spaces".
Dec 31, 2020 at 0:29 comment added Anton Petrunin Do you know, what is the source of this proof?
Dec 17, 2009 at 7:36 comment added Gjergji Zaimi A possible hint: Let Y be the complement of $X_{\delta}$. Now form $X'$ as all $ax$ with $x\in X,a\in [0,1]$, similarly for $Y'$. What can be said about $X',Y'$ and $\frac{X'+Y'}{2}$ as subsets of $\mathbb{R}^{n+1}$?
Dec 14, 2009 at 4:36 comment added Anton Petrunin (1) I do not know a proof of first problem which use Brun--Minkowski :( Can you give a hint? (2) Second problems looks nice --- I have to think a bit :)... Thank you
Dec 14, 2009 at 2:38 history edited Gjergji Zaimi CC BY-SA 2.5
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Dec 13, 2009 at 10:21 history answered Gjergji Zaimi CC BY-SA 2.5