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Lesson 1: Week 7

# Intro to curves

In daily language, we all use the word curve to mean "not straight" but does the word curve have the same meaning in math? Can a straight line be a curve? Also, what makes a curve a 'simple curve'? Created by Aanand Srinivas.

## Want to join the conversation?

• At the last , I would call it an Open Curve , because it is not closed or does not start from one point and end at the same point later. Do you agree?
• oh and the question, the spiral is a simple ,and is not crossed.
• wow.i never knew THIS existed!
• Is this spiral a curve? Or is it just a curly line?
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• yes it continues until it ends.
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• Definition of curve is "A curve is a shape or a line which is smoothly and continuously drawn in a plane having a bent or turns in it". So according to the definition of curve, can we say that any 2D shapes or plane figures are also a curve in geometry?
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• No, because a) there may be no “gaps”, and b) the curve must have a start and end.

For example an infinitely long straight line does not have a start and end. A ray has a start but no end point.

Sometimes a single point is considered a “curve”, sometimes a single point is not considered a curve, because you don’t “travel” any distance with “the pen”.

Filled areas (e. g. a plane) are not curves because a line has no width. You cannot reproduce the filling with something that occupies no space.
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• If I am right Curve is a line with start and end with no gaps .
Is straight line is curve ? or we are talking about line segment
cause straight line has no start and end but line segment have .
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• How is a Rectangle a curve
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• Remember: A rectangle is a shape of four lines (AB, BC, CD, and DA) of which the corners (ABC, BCD, CDA, and DAB) form right angles.

Mathematicians understand the word curve as: Any shape that can be drawn without lifting “the pen”. (The actual mathematical definition is even more complicated.)

Now, can we draw a rectangle as a curve? Well, yes. You may say, you need to use a straight ruler and protractor (for the right angles) and then lift the pen each time, but this does not matter for the mathematical meaning of curve.

If the explanation with a pen does not work for you, use a piece of string like a thread made of cotton to patch your clothes. If you can create the shape by laying the string on a surface, it is a curve. You may not cut the string though! It must be one string, not two strings.
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• how to find that it is a open curve or closed cure
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• soooo.... the straight line is curve or not, this has confused me...
• `Is there a more sophisticated way to say "not" simple curve?` At , it's mentioned that there is, but WHAT IS IT?