What is the difference between a normal line and a tangent line?

[mathmann]

What is the difference between a normal line and a tangent line?

 

[quantumdude]

A line is tangent to a curve if:

1. They both meet at some point.
2. They both have the same slope at that point.

A line is normal to a curve if:

1. They both meet at some point.
2. They are perpendicular to each other at that point.

 

[neutrino]

A line is tangent to a curve if:

1. They both meet at some point.
2. They both have the same slope at that point.

Addendum to 1: They meet at only one point.

 

[Data]

Addendum to 1: They meet at only one point.

Not quite. The line $y=1$ is tangent to the curve $y=\sin{x}$, but they intersect each other at infinitely many points!

 

[neutrino]

Not quite. The line $y=1$ is tangent to the curve $y=\sin{x}$, but they intersect each other at infinitely many points!

Yes, you're right.

Then, I guess someone needs to correct this Mathworld article

The word "tangent" also has an important related meaning as a line or plane which touches a given curve or solid at a single point. These geometrical objects are then called a tangent line or tangent plane, respectively.

 

[Data]

Yes, they do! The article on "tangent line" gets it right, however .