Main content

### Course: Geometry (all content) > Unit 3

Lesson 4: Curves and polygons# 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?(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)
- Is this spiral a curve? Or is it just a curly line?(1 vote)
- 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)