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What is ruler replacement theorem? I haven't heard of this theorem before. It is from geometry, which has some relationship with the coordinate system$\chi(\cdot)$ or $\xi(\cdot)$, something like that.

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If you haven't even heard of the theorem, then what prompts you to ask about it? Share some context with us, please. –  Henning Makholm Jan 22 '12 at 20:22
Google gives one hit for "ruler replacement theorem" (with the quotes). See page 42 here: math.nus.edu.sg/~matwyl/geometry_ancient_to_modern_notes.pdf –  David Mitra Jan 22 '12 at 20:25
breezy, do you know about accepting answers to your questions on this site, how to do it and why it's important? –  Gerry Myerson Jan 22 '12 at 22:34
Thank you for your answers. Somebody else gave me some problems about geometry, one of them is to prove this theorem. I did not find this theorem on google, so I ask here. I don't know about "accepting answers to your questions" on this site. What does it mean? I am new here, and I think this is a good place to discuss math problem. –  breezeintopl Jan 23 '12 at 2:26

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