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let $f:[0,1]\longrightarrow [0,1]$ be a continuous function such that $f(0)=f(1)$, show that : if the number $l$ is not of the form $\dfrac{1}{n}$ there exsits a function of this form on whose graph one cannot inscrible a horizontal chord of length $l$

This problem is from $Mathematical Analysis (Zorich) P170,problem 7(2),Thank you evryone

math110
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    Can you clarify what is meant by "inscribe in a horizontal chord"? – Eric Auld Jul 26 '13 at 01:31
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    Oh,Thank you everyone,and This problem is old one,http://math.stackexchange.com/questions/36765/constructing-a-continuous-function-whose-graph-seems-special?rq=1 – math110 Jul 26 '13 at 01:44

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