How can we mathematically differentiate between a straight line and a curve?

In summary, the conversation is about how to prove that a line is a curve. The person asking the question is unsure of how to do so and is seeking immediate help. Another person suggests clarifying the definitions of "line" and "curve" for a more precise discussion. The original poster then realizes that a straight line and a curve are different and asks for assistance in explaining this mathematically.
  • #1
Momi
1
0

Homework Statement



How to prove line is a curve?

The Attempt at a Solution



I only know that line is a straight curve but how it can be proved?no idea!
Immediate help would be appreciated...:smile:
regards,
Momi
 
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  • #2
Can you provide more context of the question and your "definitions" of "line" and "curve"?
Otherwise, the discussion isn't going to very precise... and you won't end up with a proof.
 
  • #3
O didn't know that u could call a line for a curve, even a line segment would be a curve so it don't need to be continuous ..

http://en.wikipedia.org/wiki/Curve
 
  • #4
I'm sure what you mean is that a curve and a straight line are different to you because, well, a straight line goes straight and a curve line changes directions. Put this into mathematical language!
 

1. What is the definition of a curve?

A curve is a continuous and smooth line that deviates from a straight path.

2. How do you prove that a line is a curve?

To prove that a line is a curve, you can use the definition of a curve and show that the line meets all the criteria, such as being continuous and smooth.

3. Can a straight line be considered a curve?

No, a straight line is not considered a curve because it does not deviate from a straight path and is not continuous or smooth.

4. What mathematical properties are used to prove that a line is a curve?

To prove that a line is a curve, mathematical properties such as continuity, differentiability, and smoothness are used. These properties can be determined through calculus and analysis.

5. Why is it important to prove that a line is a curve?

Proving that a line is a curve is important because it helps us understand and analyze the behavior of the line, and can also have practical applications in fields such as physics, engineering, and computer graphics.

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