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Originally posted by UnixFE
Hey folks I need your help with a math question. I have learned (and never dared to question) that a diagonal in a rectangle is shorter. So if I have a rectangle with a side length of 10x10 cm walking the diagonal will just cost me 14.14..cm instead of 20 cm around the sides. So I've learned it and so I can measure it with a ruler.
But tonight I though about the 'why is it so' and couldn't sleep anymore.
Please take a look at this picture (quick drawing with paint so please excuse the hand drawn style):
If I walk along the brown line I will still have to go 20cm although I'm already moving kind of diagonal through the rect. If I cut this into half again and move along the red line it will still be 20cm. Now I can play this game nearly endless and always will end with 20 cm although I'm reached a nearly perfect diagonal.
If there is no physical limit (atoms/quarks...) I can do this infinitely and never reach the point where 20cm 'converts' into 14.14cm right?
And if there is a physical limit (I can't split the atom..) than isn't this also a limit for me walking this line? Why can I walk the diagonal if I have to move inside our physical world? Where is the point that my infinite stairway becomes a diagonal? Is it just a hypothetical model that we can't understand and simply is correct because it is so?
edit on 3-7-2012 by UnixFE because: (no reason given)
I have learned that a diagonal in a rectangle is shorter.
Originally posted by Phage
You are flirting with the idea behind integral calculus with the concept of infinitely small intervals but Pythagoras gets to the answer a bit simpler.
Originally posted by Wide-Eyes
reply to post by Domo1
I don't know how much beer you've had but even after ten pints, I can still walk in a straight line. Thus, the distance from A to C is shorter than wobbling around in a zig-zag pattern. I don't get it, walk in a straight line dammit!