It is very common to confuse these two concepts: circumference and circle. Although both are closely related, the difference between them is very large. They are two geometric concepts that are related but should not be confused.
Both have in common the round shape that we all know. Broadly speaking, we could say that the circumference refers to the “edge”, while the circle is the “edge plus the interior”.
The rigor of Mathematics and therefore of Geometry does not allow us to define its objects of study just like that. For example, when we talk about something round and flat, we immediately relate it to the circle, this only serves to exemplify a mathematical object with something concrete so that a child understands it. The reality is that mathematical or geometric objects are “ideal” not “concrete” so when we give an example and relate them to real things we must take into account that this object is not a circle or a circumference or a square, it is simply something that resembles the true circle or circumference or square that they are objects that only exist in the mind.
When we draw a circumference or a circle or a square, for example, we are making a representation in the plane of that ideal object. When we say that this jar of tomatoes is a cylinder, we should say that this jar of tomatoes is shaped like a cylinder, it is not a cylinder. This is mathematical rigor.
Now we will show you what is the difference between circumference and circle.
What do you need
- Recognize the difference between these two concepts
- Relate circumference and circle with perimeter and area.
- Pencil, compass and paper to represent them.
- Calculator to calculate perimeters and areas.
Instructions
- As we explained before, the circumference and the circle are ideal mathematical objects, they exist only in the minds of people but we must use representations to be able to take them to the plane of the paper, to the earth, to space or to relate them to real and concrete objects., which can be seen and touched, to learn about them, differentiate them, be able to exemplify and make calculations of areas and perimeters.
- Already the philosophers and mathematicians of antiquity discussed and were concerned about knowing what was the relationship between the circle and its diameter. Everyone was trying to find out why when they divided the outline of the circle by its diameter they got the same quotient, regardless of the size of the circle. The girth-diameter ratio was a number close to three. Thus arose this irrational number that we all know as the number Pi, in Greek ∏
- Let’s clarify some concepts:
- Circumference: “It is the set of infinite points that are equidistant from another called center.” This gives us the idea that the circumference is just a dotted line, an outline, an edge, in simple words it is hollow.
- The radius of the circle is the distance from the center to one of its points (any since they are all at the same distance from it).
- The diameter is the distance between two of its points passing through the center, in other words the diameter is twice the radius or the radius is half the diameter.
- The circle is all the surface that encloses the circumference. We can also say that the outline or edge of the circle is a circumference. The circle, like the circumference, has a radius and a diameter.
- Finally we will see what we can calculate for each one: perimeter or area?
- If we refer to a circumference, we can only calculate its perimeter or contour since there is nothing inside it, so it would be impossible to calculate area (remember that area implies a flat surface and circumference does not). The diameter (D) or the radius (r) and the number Pi intervene in the perimeter of the circumference: Perimeter = ∏. D or Perimeter = 2. ∏. r
- The number ∏and the radius intervene in the area of the circle: Area = ∏. r2 _
Tips
- When you have to calculate perimeters and areas, you must be very clear that the perimeter refers to the edge or contour, instead the area inside the geometric figure, for example, it is impossible to calculate the area of the circumference.
- Get used to calling things by their correct name, comparing, differentiating to accurately recognize and name the names of Geometry objects, as in this case circumference and circle.