Proving Pi

Williams, Gwendolyn D.             Paul Robeson High School
                                   (312) 723-1700
                           

Objectives:
To show the ratio of pi by revolving a circle one complete time.
The students will learn why the ratio is true.
To allow the students to do the same independent of the teacher's 
help.
  
Apparatus needed:
You need: Two random size pieces of plexiglass.
          One screw (long enough to pass through all thickness of the 
          pieces you use)
          One pair of nuts to hold the screw in place.
          One aluminum channel no longer than four feet.

Recommended Strategy:
To make the circle, cut either piece first.  Draw a circle on the 
paper covering of the plexiglass or cut random tangents to a squared 
piece until it is it is somewhat round.  Drill a hole at the center of 
the piece large enough to put your screw through.  Finding the center 
should not be a problem.  Once the "round" piece is ready, sand out 
the rough spots.  Find a thick piece of wood that you can nail the 
circle to .  After nailing the circle to the wood, go to the sander 
and rotate the plexiglass until the rough spots are gone.  Draw an 
arrow from the center to the edge of the circle (a radius).  The 
second piece will be used for the handle and the spacers.  Cut three 
pieces, two of the same length and long enough to extend from the 
center of the circle to the outside and the other about one inch 
shorter.  The first two pieces should be wide enough to fit 
comfortably in your hand as they will be used to guide the circle 
through the channel.  The third piece will be used for spacers.  Drill 
the same size hole near the end of the two pieces to be used for the 
handle and two holes four inches apart in the piece to be used for 
spacers. Do not cut before the holes are drilled.  At this point get 
help from the shop manager to assist in putting the final product 
together.  If it is not obvious, the spacers should be cut to fit one 
under each handle and flush against the circle to reduce friction when 
rotating.  Use other scrap pieces to space the edge of the handle that 
will be held in your hand.  Sand all edges.  Use the glue to hold the 
spacers in place at the edge of the handle.  For the classroom demo, 
the aluminum channel will be placed on the desk or table.  Stand the 
circle on its side, arrow down and perpendicular to the channel.  Mark 
the origin with a pencil on the channel.  Make a complete rotation of 
the circle.  At the end of this rotation, mark the channel again.  To 
find this length, do either of two things.  Lay the circle on the 
channel end over end from the origin to the end of the length at which 
time the measure is obvious.  Or lay the circle between perpendiculars 
for as many times as it takes to cover this length.  In either case, 
the measure should be 3.14159... or a number very close to that.