I have tried to get some help w/ this problem from other people
but no one has helped me out yet.
Suppose that for each irrational p, an equilateral triangle T_p
(including its interior) is constructed in the plane with one vertex
at (p,0) and its opposite side above and parallel to the x-axis.
Prove that Union{T_p:p in P} (P: irrationals) must contain a rectangle of the form [a,b] x (0,1/k] for some a, b in R and
some k in N.
In the hypothesis, we could weaken “equilateral” to read “ ... ” ?
(Hint: Consider N_k = { p in P : T_p has height >= 1/k })
Thank you.
2006-12-14
18:22:01
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2 answers
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asked by
jbs
1
in
Mathematics