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Jul 28, 2013 at 17:08 vote accept CommunityBot
Jul 28, 2013 at 16:10 history edited Alexandre Eremenko CC BY-SA 3.0
added 48 characters in body
Jul 28, 2013 at 16:05 comment added Alexandre Eremenko Silvi: thanks, I corrected the error.
Jul 28, 2013 at 16:04 history edited Alexandre Eremenko CC BY-SA 3.0
added 12 characters in body
Jul 28, 2013 at 15:13 comment added user37834 @Alexandre: Reading the necessity part of you nice answer tells me you should edit the first line of your answer. I think you meant $\frac{\sum x_j}{n} = \frac{a+b+c}3$.
Jul 28, 2013 at 11:34 comment added Alexandre Eremenko About barycenter: second expression. It is also called the center of gravity. About affine function: take any one which is 0 at A and 1 at B.
Jul 28, 2013 at 9:16 comment added user30300 First, By the barycenter of $x_j$, you mean $\sum x_j$ or $\frac{\sum x_j}{n}$ ? Second, would you give a tip on how do you construct the affine function claimed in the last line of your answer.
Jul 28, 2013 at 7:54 history answered Alexandre Eremenko CC BY-SA 3.0