Any line is a curve. Line can be straight or bended

Curves are formed by drawing without lifting the pen from the paper

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Simple Curve
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A curve which does not cross itself is a simple curve.

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Here,

(1) & (2) are simple curves

(3) & (4) are not simple curves

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Closed
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Curve
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A curve which has no open ends is a closed curve

Here,

(2) & (4) are closed curves

(1) & (3) are not closed curves