No, they aren’t (but sometimes they are the same thing because the school books do not always establish the difference between them).
The definition of circumference is very accurate and it tells us the following: “Circumference is the geometric place of the plane points which have the same distance till they reach a fixed point.” If we have a look at the image shown below, we will notice that the circumference is the red line.
Concerning the word circle it is equivocally used in some school books. However, the circle is accepted to represent the area bounded by the circumference. Lots of Maths exercises refer themselves to a circle when they should refer to a circumference. Have a look at the image shown below and you will notice that the circle is all the green area, this is, the line that bounds the circumference and its interior.
When the definition of circumference refers to it as being the geometric place of the plain points that have the same distance till they reach a given point, we have to understand that this distance means a number superior to zero. So, a point is neither a circumference nor a circle.
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