ON THE STEINHAUS TILING PROBLEM FOR Z3

On the Steinhaus tiling problem

We prove several results related to a question of Steinhaus: is there a set E ⊂ R such that the image of E under each rigid motion of R contains exactly one lattice point? Assuming measurability we answer the analogous question in higher dimensions in the negative, and we improve on the known partial results in the two dimensional case. We also consider a related problem involving finite sets o...

Survey of the Steinhaus tiling problem

Comments about the Steinhaus Tiling Problem

Recently, using Fourier transform methods, it was shown that there is no measurable Steinhaus set in R3, a set which no matter how translated and rotated contains exactly one integer lattice point. Here, we show that this argument cannot generalize to any lattice and, on the other hand, give some lattices to which this method applies. We also show there is no measurable Steinhaus set for a spec...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Steinhaus’ Problem on Partition of a Triangle

H. Steinhaus has asked whether inside each acute triangle there is a point from which perpendiculars to the sides divide the triangle into three parts of equal areas. We present two solutions of Steinhaus’ problem. The n-dimensional case of Theorem 1 below was proved in [6], see also [2] and [4, Theorem 2.1, p. 152]. For an earlier mass-partition version of Theorem 1, for bounded convex masses ...