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

[mymachine]

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

Thank you

 

[Mark44]

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.

 

[JJacquelin]

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.

 

[Mentallic]

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.

 

[Mark44]

Of course, you can : First, buy a compass with infinitely long legs.

Where do you buy one of these?

Then, go to the infinity. There put the sharp point and turn the compass : Very far from there, the straight arc is drawn.

 

[JJacquelin]

Where do you buy one of these?

You may ask Alice. She knows a good shop in Wonderland.