Dear Mathematicians.. a question for you.

Originally posted by socialist
reply to post by charlyv

 

An ideal circle has no straight lines.

The tangent line to a circle has some interesting properties. There is a unique point P which lies on both the line and the circle. Now take a point Q lying on the same line so that PQ has non-zero length. Let C be the center of the circle. By the Pythagorean theorem CQ > CP. Therefore Q does not lie on the same circle as P. This is true regardless of how small PQ gets. No matter how closely you "zoom in" only one point on the circle is ever going to touch the line. Aren't ideal objects wonderful?

Ooh, pretty picture.

Don't forget being perpendicular to the radius at the point of tangency, which is why CQ > CP, it's the hypotenuse of the right triangle CPQ with P being the right angle.

Originally posted by PurpleChiten

Originally posted by socialist
reply to post by charlyv

 

An ideal circle has no straight lines.

The tangent line to a circle has some interesting properties. There is a unique point P which lies on both the line and the circle. Now take a point Q lying on the same line so that PQ has non-zero length. Let C be the center of the circle. By the Pythagorean theorem CQ > CP. Therefore Q does not lie on the same circle as P. This is true regardless of how small PQ gets. No matter how closely you "zoom in" only one point on the circle is ever going to touch the line. Aren't ideal objects wonderful?

Ooh, pretty picture.

Don't forget being perpendicular to the radius at the point of tangency, which is why CQ > CP, it's the hypotenuse of the right triangle CPQ with P being the right angle.

Yes, which produces an asymptotic line , unresolved from a straight line with infinite zoom.
The nature of this world.