Abstract
The answer to the similar plane problem is four and it was expected that a finite, rather small number, ten or twelve, would be the answer to the above problem. I shall show that actually the answer is infinity. Take rectangular coordinate axes and in the vertical plane XOZ draw a polygonal line A0A1A2..., from AQ(l, 0, 0), above OX, convex downwards, of total length less than and such that the angle between the directions OX and AnAn+1 is greater than fw for any n. 00
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