Friday, 11 October 2013

regular 9-gon

Let each of the vertices of a regular 9-gon be colored black or red.
(i) Show that there are two adjacent vertices of the same color.
(ii) Show that there are three adjacent vertices of the same color forming an isosceles triangle.  

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Define f:RR by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...