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>> if you have 2 vectors a and b of length n is it true that the euclidean
>> distance between the two is greater than the euclidean distance between
>> them if each of their elements contained their means. it seems this
>> way..
>>
>> if d( (a1,a2),(b1,b2) ) >= d( ((a1+a2)/2, (a1+a2)/2), ((b1+b2)/2,
>> (b1+b2)/2) )
>
> Do you mean for R^2? The question depends on what dimensional space you
> are
> talking about...
if the OP means R^2, i would suggest a transformation in pole-coordinates
a1 = n*cos(alfa)
a2 = n*sin(alfa)
b1 = n*cos(beta)
b2 = n*sin(beta)
if you write that out, you will see that the statement is correct
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