Differentiate between Closed curve and Simple closed curve with example
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Answer:
Triangle, quadrilateral, circle, etc., are examples of closed curves. A curve which starts and ends at the same point without crossing itself is called a simple closed curve. ... A closed curve which does not cross itself is called a simple closed curve. The curve which crosses itself is not a simple closed curve.
Answer:
Simple means it doesn’t intersect itself. Closed means that it ends where it starts (or rather, it has no start or end, but is bounded) so it divides the plane into two regions.
One can formally define a continuous curve as a continuous function, f, from the interval [0, 1] to the plane. So, for a closed curve f(0) = f(1). Then the curve is simple if there are no two points p and q (except possibly 0 and 1) such that f(p) = f(q).
Triangles, quadrilateral,circle,etc are examples of closed curves. The shape which is not closed by line segments or a curve is called an open curve . A closed curve which does not cross itself is called a simple closed curve . The curve which crosses itself is not a simple closed curve.