How To Create An Arc Of A Circle As A Straight Line?

mymachine
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How do you construct the arc of the circle as a straight line by geometry not by an equation?

Thank you
 
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mymachine said:
How do you construct the arc of the circle as a straight line by geometry not by an equation?
You can't. An arc of a circle is not a straight line. The geometrical way to construct a circle is to use a compass, which is not the same as the compass that is used to determine magnetic north. The compass I'm referring to has two legs that are hinged. One leg has a sharp point, and the other has a pencil or pen.

The end with the point is fixed, and the other end is used to draw the circle.
 
Mark44 said:
You can't. An arc of a circle is not a straight line. The geometrical way to construct a circle is to use a compass, which is not the same as the compass that is used to determine magnetic north. The compass I'm referring to has two legs that are hinged. One leg has a sharp point, and the other has a pencil or pen.
The end with the point is fixed, and the other end is used to draw the circle.

Of course, you can : First, buy a compass with infinitely long legs. Then, go to the infinity. There put the sharp point and turn the compass : Very far from there, the straight arc is drawn. :devil:
 
Last edited:
mymachine might be asking how to construct a line 2\pi r units long given the circle with radius r.

I don't believe it can be done because of a similar argument for why you cannot square the unit circle - i.e. to find a square with side length \sqrt{\pi} by geometric constructions.
 
JJacquelin said:
Of course, you can : First, buy a compass with infinitely long legs.
Where do you buy one of these?
JJacquelin said:
Then, go to the infinity. There put the sharp point and turn the compass : Very far from there, the straight arc is drawn. :devil:
 
Mark44 said:
Where do you buy one of these?
You may ask Alice. She knows a good shop in Wonderland.
 

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