For curves that enclose a region, the dimension can be obtained by the
comparing the perimeter of the curve and the area of the enclosed region, 
P = k⋅A^{d/2}. 
We illustrate this relation for simple Euclidean curves. 


Next, we show why the same relation cannot hold for fractal curves. 
If the dimension, d, of the curve satisfies d > 1, then the perimeter is infinite yet the enclosed
area is finite. 
Consequently, P = k⋅A^{d/2} cannot hold.  

Then we reexpress the Euclidean approach to obtain a form that can
be applied to fractal curves. 
Looking at geometrically similar shapes and measuring the area and perimeter
at the same scale, we find 
P_{1}/P_{2} = (A_{1}/A_{2})^{d/2} 


Here is an example of using the relation between perimeters
and areas to calculate the dimension. 
