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Course: Class 6 > Unit 6
Lesson 2: Basic geometrical ideas 4.2Intro 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)
- 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)