How to determine the value of pi.
First approximation. 6 chords
Draw a circle and inside it draw 6 equatorial triangles.
Add up the six chords that lie near the circumference and divide by
pi = 6 / 2 = 3
Second approximation 12 chords
Bisect one of the 60 degree angles with a radius.
Compute the length of each segment of that radius.
Compute the chord length of 1/12 of the circle. use the
right triangle with sides of
.5 and 0.133975.
Multiply the chord length times 6 ( one half the number of
chords) to get. 0.51763809 X 6 = 3.105828541
Third approximation 24 chords
Bisect one of the 30 degree angles with a radius.
From the last approximation the chord length is 0.51763809
H or half the chord length is 0.258819045
L = SQRT( 1^2 - H^2 ) or 0.99144866
s = 1 - L
The new chord = SQRT( s^2 + H^2 ) = 0.261052384
Compute the new chord X 12 = 3.1322628608
Repeat the above for more accuracy.
SUMMARY of results
6 Chords pi = 3
12 chords pi = 310582
24 chords pi = 3.13262
48 chords pi = 3.13935
96 chords pi = 3.14103
Return to Home Page