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Math Help - Linear Algebra. Ptolemy's inequality in R^n

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    Linear Algebra. Ptolemy's inequality in R^n

    Let x,y,z,t belongs to R^n where d(x,y)=||x-y||. Show that(Ptolemy's inequality): d(x,y)d(z,t)
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    Quote Originally Posted by ypatia View Post
    Let x,y,z,t belongs to R^n where d(x,y)=||x-y||. Show that(Ptolemy's inequality): d(x,y)d(z,t) + d(y,z)d(t,x) ≥ d(x,z)d(y,t).
    You will find a neat proof of that here (pdf file: it's a research paper published in Pacific J. Math., so be warned that it may not be that easy to read, with some steps left for the reader to fill. The result that you want is Theorem 1, on the second page.)
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