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-   -   Concentric circles in Q10 (http://book.caltech.edu/bookforum/showthread.php?t=926)

IsidroHidalgo 04-21-2013 08:11 AM

Re: Concentric circles in Q10
 
But I finally don't have a clear idea of the center of our hypothesis here: is always x_1=0 and x_2=0 or not?

Elroch 04-21-2013 08:56 AM

Re: Concentric circles in Q10
 
Quote:

Originally Posted by IsidroHidalgo (Post 10529)
But I finally don't have a clear idea of the center of our hypothesis here: is always x_1=0 and x_2=0 or not?

Well, x_1 and x_1 are the variables, but the centre is at (0,0) as indicated in yaser's post #2.

marek 04-21-2013 09:56 AM

Re: Concentric circles in Q10
 
You can choose your points however you want. So fix any layout of points by drawing them on a piece of piece of paper. If you translate all the points by moving that piece of paper around, the new positions are another set of points which you could have chosen.

So in a sense you can consider any layout of points and then start the circles where ever you wanted. The trick is that once you pick a spot for the centers of the circles you have to keep that same center for all the dichotomies you're generating.

And that does also mean that you can assume one point is in the center if you want.

IsidroHidalgo 04-21-2013 10:26 AM

Re: Concentric circles in Q10
 
But he says to in #5 "so the origin is effectively arbitrary", so there's a little confusion here for me...

marek 04-21-2013 11:06 AM

Re: Concentric circles in Q10
 
Quote:

Originally Posted by IsidroHidalgo (Post 10534)
But he says to in #5 "so the origin is effectively arbitrary", so there's a little confusion here for me...

That's what I'm trying to address in my above post.

Let me make my analogy a little more substantial. Let's say your grid and origin are fixed on your desk. The paper you draw your points on is transparent. You can slide around that transparency as you want, since your choice of points is up to you. But from the perspective of the points on the transparency, the points are fixed but the origin is sliding around. That is what he's referring to by saying the origin is effectively arbitrary.

Once you pick your points, you can put your origin anywhere you want (though the actual mechanic is that you're making new set of points that are appropriately translated with respect to the origin and using them instead)


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