Thread: Geometric "Pi Segement Construction" algorithims?

Can anybody explain to me some of the methods used to approxiamtely construct a line segement of length ????

Thanks in advance

scroll down to III Exercises/Solutions , part D

What They Don't Tell You About Pi in High School

Dear mfetch22,
Pi is approx 22/7. Draw a line = to 22 inches mark AB. At A draw a ray of an acute angle. Starting at A scribe with a compass 7 equal segments ending in C. Connect BC and then draw lines parallel to BC thru each scribe mark intersecting AB.Each segment on AB = pi


bjh

Hello, mfetch22!

Can anybody explain to me some of the methods used
to approxiamtely construct a line segement of length ?

We can always construct a angle.
Construct an equilateral triangle and bisect one of its angles.

Code:

                A
              * o *
          *     |  o  *
        *       |     o *
       *        |1       o
                |           o
      *         |         *    o
      *         *O        *       o
      *        /|         *          o
            1 / |                       o
       *     /30|        *                 o
        *   /   |1      *                     o
          */    |     *                          o
  P - - - + - * * * - - + - - - - - - + - - - - - - o - - Q
          C     B       D             E             F
          : - -  1  - - : - -  1  - - : - -  1  - - :

We have a circle with center and radius 1.
is a diameter.
Line is tangent to circle at

Construct segment so that

From , mark off three radii on
. .

Draw segment

We have: .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


Proof

In right triangle

Then: .


In right triangle

. .


Therefore: .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


From: .Mathematical Puzzles and Pastimes, Aaron Bakst
. . . . . . . . D. Van Nostrand Company, Inc., 1954