The circumference of a circle is proportional to the diameter , and we can write this relationship as . The circumference is also proportional to the radius of the circle, and the constant of proportionality is because the diameter is twice as long as the radius. However, the area of a circle is not proportional to the diameter (or the radius). 

The area of a circle with radius is a little more than 3 times the area of a square with side so the area of a circle of radius is approximately . We saw earlier that the circumference of a circle of radius is . If we write for the circumference of a circle, this proportional relationship can be written .

The area of a circle with radius is approximately .  Unlike the circumference, the area is not proportional to the radius because cannot be written in the form for a number . We will investigate and refine the relationship between the area and the radius of a circle in future lessons.