# A covering problem

1. May 3, 2004

### dapet

Because the administrators recomend to post the topics from classical geometry here, there's one covering problem, that I've tried to generalized (still without success) one simpler task:

How to cover the plane by cyclic tetragons T_1, T_2,... (a tetragon is called cyclic if it's possible to circumscribe it a circle) that resemble to the given cyclic tetragon T, so that for each i<>j tegragons T_i and T_j are similar, but they don't coincide.

note: easier problem is to cover the plane by similar rectangulars....

I don't know how to start, e.g. if T isn't a rectangle we can find tetragons T_i and T_j that form an isosceles trapezoid and then it suffices to cover the plane by similar isosceles trapezoids... but this is too litle to solve the problem. Can anybody help? Thanks...

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