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yufeizhao.wordpress.com | ||
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xorshammer.com
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| | | | | Take a real number, $latex x$. Write out its continued fraction: $latex \displaystyle{x=a_0+\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+\cdots}}}}$ It's an intriguing fact that if you look at the sequence of geometric means $latex a_0, (a_0a_1)^{1/2}, (a_0a_1a_2)^{1/3}, \ldots$ this approaches a single constant, called Khinchin's constant, which is approximately $latex K\approx 2.69$, foralmost every $latex x$. This means that if you... | |
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jeremykun.wordpress.com
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| | | | | Define the Ramsey number $ R(k,m)$ to be the minimum number $ n$ of vertices required of the complete graph $ K_n$ so that for any two-coloring (red, blue) of the edges of $ K_n$ one of two things will happen: There is a red $ k$-clique; that is, a complete subgraph of $ k$... | |
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www.jeremykun.com
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| | | | | Define the Ramsey number $ R(k,m)$ to be the minimum number $ n$ of vertices required of the complete graph $ K_n$ so that for any two-coloring (red, blue) of the edges of $ K_n$ one of two things will happen: There is a red $ k$-clique; that is, a complete subgraph of $ k$ vertices for which all edges are red. There is a blue $ m$-clique. It is known that these numbers are always finite, but it is very difficult to compute them exactly. | |
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cambridge163.wordpress.com
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| | | This is the excerpt for your very firstpost. | ||
