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

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Homework Help Overview

The discussion revolves around the definitions and distinctions between normal lines and tangent lines in the context of curves. Participants are exploring the geometric properties of these lines and their relationships to curves.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants attempt to define tangent and normal lines based on their intersection points and slopes. There are questions regarding the accuracy of these definitions, particularly concerning the nature of tangents and their intersections with curves.

Discussion Status

The discussion includes various interpretations of tangent lines, with some participants questioning the completeness of definitions provided. There is acknowledgment of differing views on the nature of tangents, particularly in relation to the sine function, indicating an ongoing exploration of the topic.

Contextual Notes

Some participants reference external sources, such as a Mathworld article, to support their definitions, suggesting a need for clarity in the terminology used in mathematical literature.

mathmann
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What is the difference between a normal line and a tangent line?
 
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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.
 
Tom Mattson said:
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.
 
neutrino said:
Addendum to 1: They meet at only one point.
Not quite. The line [itex]y=1[/itex] is tangent to the curve [itex]y=\sin{x}[/itex], but they intersect each other at infinitely many points!
 
Last edited:
Data said:
Not quite. The line [itex]y=1[/itex] is tangent to the curve [itex]y=\sin{x}[/itex], 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.
 
Yes, they do! The article on "tangent line" gets it right, however :wink:.
 

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