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Nowadays with computers, Compass-and-straightedge construction doesn't look useful from my point of view. Probably I am just too narrow-minded, So I'm just curious, could anyone tell me any applications of Compass-and-straightedge construction, even in terms of mathematical theory?

Thanks!

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What about mind stretching? Geometry is truly unique in this matter... –  dtldarek Sep 17 '13 at 21:50
    
You are right, they are no longer essential drafting tools. Might be handy on a small boat at sea, when the batteries die. In schools one has to worry about people stabbing each other. Virtual compasses are safer. –  André Nicolas Sep 17 '13 at 21:57
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It's important because it's the practically the only opportunity we have to introduce deductive proof based mathematics within an axiomatic system to high school students. Unless students go on to be math majors in college, it's likely that they will go through their entire mathematical education never learning that they've only been learning applied math the entire time, never being introduced to what doing real mathematics is actually like. –  David H Sep 17 '13 at 22:17
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