Intermath: Investigations: Geometry: Circle

What happens to the circumference of a circle if you double the diameter? If you triple the diameter? If you halve the diameter? As the diameter increases (or decreases) in measure, how does the circumference change? Why does this change occur?

(This change will be shown
with Geometer's Sketchpad. Please note that the circles constructed
are double and triple the diameter of the innermost circle. The
points that can be used to adjust the size of the circles are
only the **blue** points. Note how the measurements change
as the size is adjusted.)

Looking at the sketch
below the diameters' measures are given to show that they are
in accordance with the problem above. The corresponding circumferences
to these diameters are given out to the side of the corresponding
diameter. From looking simply at the measurements' ratios, it
is clear that there is a distinct relationship between the increase
in diameter length and the increase in circumference. It is in
accordance with the proportion of the original cirlce *x*.

Now to make sense of what
can be seen. First, think of the equation for the circumference
of a circle. Circumferece = 2**pi**radius. Continuing this,
we can simplify the equation with simple substitution. Knowing
that diameter = 2*radius, Circumference also equals *pi**diameter.
Given that the only variable in the equation is the diameter of
the circle, the circumference would vary along with only that
variable.