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if we start from just above point and go up and end at just below point how is the curve not simple curve. ncert class 6 chapter 4 pg 72 says it is not http://ncert.nic.in/textbook/textbook.htm?femh1=4-14 please help

I am a student and trying to understand things it is a 8 like figure this question is not off topic as it is a maths question. don't gang up on me pls. I am not up at your level also I cant understand your big terms I don't understand why people reporting me I also need help .pls no teacher is answering me properly .Pls help .

Consider this:

The blue curve on the right is a simple closed curve, also called a Jordan curve.

The red curve on the left is a closed curve, but is is not simple, because it intersects (crosses) itself. It does not matter where it crosses itself.

You can think of it this way: When you draw the curve, and you need to cross or overlap the already drawn part of the curve (except at the very end or start), it cannot be a simple curve. The only place where a closed simple curve overlaps, is at the starting and ending point.

If you make the mistake of starting drawing the curve exactly where it starts, the above thought model is a bit broken. You do not get to cheat that way; such curves are still not simple. Consider the above way of thinking about it only valid, if you start the curve at a point that is not close to an intersection.

You can draw it as large as you need, with as sharp pen or pencil as you need, to check if some parts are just very close, or really intersect/cross/overlap. Only a real intersection/crossing/overlapping matters: you can think of having a very, very sharp pen/pencil and a huge area to draw on.

A simple curve does not need to be closed, it can be open as well. (Simple open curves are also called Jordan arcs.) Such curves do not cross themselves, nor do they end where they staryed. For example, $alpha$ is not a simple curve, because it crosses itself; but $nu$ is simple.

Furthermore, $rho$ is not a simple curve, because it starts (or ends, depending on which way you draw it) at the middle of itself; it does cross/intersect itself.

The proper mathematical term for when a curve crosses itself is "self-intersecting". Thus, every curve is either "simple" or "self-intersecting".

Note that a closed curve must start and end at exactly the same point. It is not enough for the curve to look closed. For example,

is indeed an open simple curve. However, you cannot close it but keep it simple it by moving the endpoints closer to the vertical part. No matter how close you put the endpoints, the two points will be separate (distinct), unless you cross the vertical part. If you cross the vertical part, the curve is no longer simple.