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```					                                               DISCOVERING PI
THE HISTORY OF PI

The ratio of the circumference of the diameter of a circle is constant and has been recognized for as long as we have written records.
A ratio of 3:1 is even mentioned in the Old Testament:

And he made a molten sea, ten cubits from the one brim to the other: it was round all about and his height was five cubits: and a line
of thirty cubits did compass it about. (I Kings 7, 23; II Chronicles 4, 2)

However the first theoretical calculation of a value of pi was that of Archimedes of Syracuse (287-212 BC), one of the most brilliant
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mathematicians of the ancient world. Archimedes worked out that              .         Archimedes’ results rested upon
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approximating the area of circle based on the area of a regular polygon inscribed within the circle. Beginning with a hexagon, he
worked all the way up to a polygon with 96 sides.

INVESTIGATION

1.       Construct segment AB
2.       Construct point C, the midpoint of AB
3.       Construct circle CB
4.       Make the circle small
5.       Measure the circumference of the circle. Select the circle then choose Circumference from the Measure menu.
6.       Measure AB (the diameter of the circle) by selecting the segment only.
7.       Select, in order, the length measurement and the circumference measurement. Then in the Graph Menu choose Tabulate to
make a table for these measurements.
8.       Make circle a little bigger; then add the new measurement to your table by double-clicking at the top of the table. Continue
in this fashion until your table has at least four entries.
9.       Choose Plot Points from the Graph Menu and enter the coordinates of the points in your table one by one.
10.      Describe the points that appear on the graph.
11.      Construct a ray from point D (the origin) to any of the plotted points.
12.      Measure the slope of the ray.
13.      How is the slope of the ray related to the circumference/diameter ratio for the circles.
14.      What is the significance of the fact that all the plotted points lie on this ray?

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