That a circle is one-dimensional and has no surface
It’s quite intuitive, if you think about it. A circle consists of a line that turns to infinity, as expected. Another thing that makes it intuitive is when you look at the equation of a circle, which is provided by the following:
(x-h) 2+ (y-k) 2 = r2
Note that the circle is simply a graph of the solutions to the following equations and does not define the coordinates inside the shape, but only the circumference. I will provide you with a mathematical explanation. Therefore, if you are not a math lover, you are free to ignore it, otherwise read on.
The first way to determine the number of dimensions of an object is to determine the number of parameters required in its description. We find the number of dimensions in which an object is found by examining the number of variables constituting the equation, then subtracting that number from the total number of equations constituting the object. In this case, we have 2 variables.
Is not a variable since the radius of a circle does not change). We also see that there is only one equation here, which means that our object is one-dimensional. This begs the question of what do you find when you solve these Grade 6 geometry problems?
The part of the circle that includes the circumference and defines the inner part is given by the following inequality:
(x-h) 2+ (y-k) 2≤r2
This is called a disk and, unlike the circle, it is a 2D object.
How do we know it?
We see that the quantity of variables defining the object is 2, like the last time. However, we see that there are no real equations defining this, that is to say it is a dimension 2. Since it is in 2D, it has a surface.
If you are in the geometry of high school and you are in this part of the program that covers several circles, prepare to prepare it and give an example to your teacher as soon as these words escape him.