The Circumference/Diameter Ratio
In this activity you’ll discover a relationship between a circle’s circumference and
its diameter. Even if that relationship is familiar to you, the investigation may
demonstrate it in a different way.
Sketch and Investigate
1. Construct line segment AB
Select the line
segment; then in
the Construct
menu choose
Midpoint
Select point C
then point B; then
in the Construct
menu choose
Circle By Centre
+ Point
Select the circle:
then in the
Measure menu
choose
Circumference
2. Construct point C, the midpoint of AB.
3. Construct circle centre C through point B.
A
B
A
C
B
A
C
B
4. Measure the circumference of the circle.
Select points A
and B; then in the
Measure menu
select Distance
5. Measure AB (the diameter of the circle).
Select in order,
the diameter
measurement and
the circumference
measurement.
Then in the
Graph menu
choose Plot As
(x,y)
7. Plot the diameter and circumference measures as (x,y) (point H in the
diagram below). Change the scale if necessary by dragging the point on the
X-axis. Ensure only H is selected and in the Display menu turn on Trace
12
Point.
6. Make the circle small by dragging point B.
10
Circum ference
CB = 8.06 cm
8
H
AB = 2.57 cm
6
A
C
B
4
2
-15
-10
-5
5
-2
-4
-6
-8
-10
10
15
8. Drag point B to change your circle. Watch the plotted point.
9. Construct a line from the origin through the traced points of H.
Select the line;
then in the
Measure menu
choose either
Slope or
Equation
10. Find the equation or slope of the line.
How is the slope/equation of the line related to the circumference/diameter
ratio?
What’s the significance of the fact that all the plotted points lie on this ray?
The circumference/diameter ratio is represented by the Greek letter  (pi).
Write down the value of  and a formula for the circumference (C) in terms
of the diameter (d).
Write down a formula for circumference using C,  and r (radius).
Adapted from Exploring Geometry with Geometer’s Sketchpad
RonT/Circumference