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Course: Geometry (all content) > Unit 3
Lesson 4: Curves and polygonsIntro 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.
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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?(5 votes)
oh and the question, the spiral is a simple ,and is not crossed.(3 votes)- wow.i never knew THIS existed!(2 votes)
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?(1 vote)
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.(1 vote)
- Can we say that any 2D shapes or plane figures are also a curve?(1 vote)
- 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 .(1 vote) 
How is a Rectangle a curve(1 vote)- 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.(1 vote)
how to find that it is a open curve or closed cure(1 vote)
soooo.... the straight line is curve or not, this has confused me...(0 votes)- no because it is a straight line(0 votes)
Is there a more sophisticated way to say "not" simple curve?At4:14, it's mentioned that there is, but WHAT IS IT?(1 vote)- Self‑intersecting curve.(1 vote)
4:14