Lets have a nonagon with sides which are all equal. The length of the sides are integers. Does anyone know how to inscribe in it an equilateral triangle whose three vertexes intersect with the nonagon? How many such nonagons exist?
Nonagons with integer sides
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$\begingroup$
geometry
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0What do you mean "How many such nonagons exist?" Are you asking how many ways there are to put an equilateral triangle in a nonagon? Are you requiring the nonagon to be regular? – 2012-02-07
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2The nonagon is not regular because only the sides are equal. – 2012-02-07
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0To rephrase: Vassilis's desired nonagons are equilateral, but not necessarily equiangular. – 2012-02-07
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0Just to be clear, by nonagon, you mean $9$-sided, right? I sense that some might not know the Greek prefixes, and think you mean $n$-gon. – 2012-02-07
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0If any interior angles are less than or equal to $\pi/3$, it is easy to inscribe such triangles by making them small and have one edge aligned with the $n$-gon's edge. This would allow for infinitely many, if that is the kind of answer you are looking for. Now assume all interior angles are greater than $\pi/3$, if that helps. – 2012-02-07
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1@Jordan. Nonagon means 9 sides – 2012-02-07
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0@Alex.Please give me the length of the side of one of these nonagons and the length of the side of the inscribed equilateral triangle. – 2012-02-07