In honor of “pi day” (March 14, or 3/14),
here is one way to find an approximation for pi.
The value of pi will be very close to a
solution of this polynomial equation:
0=-0.5 + x/6 – x^3/1296 + x^5/933,120 – x^7/1,410,877,440
(This formula is derived from the equation
sin(pi/6) = 1/2
with sin x replaced by the first four terms
of its Taylor series approximation.)
One way to find the solution to a polynomial
equation is to create a graph to see where
the polynomial curve crosses the axis.
The graph shows that the value of pi is
a bit smaller than 3.1416.
Note: if you really are trying for greater
precision, then solve this equation:
0 = -0.5 + u – u^3/6 + u^5/120 – u^7/5040
which has the solution u = pi/6. You can
add more terms to the Taylor series if you
need more precision. Since pi/6 is less than
one the rest of the terms in the series become
very small very fast.
Happy pi day.
……………..
–Douglas Downing
You are welcome to write your comments on the facebook page at
https://www.facebook.com/DouglasADowningSPU/?ref=profile
This blog is part of the
Seattle Pacific University Political Economy blog group
(click here for index).
Click here for the index of topics for the blog
note: the previous two web addresses have changed;
the old version should still redirect to the new version
Twitter:
https://twitter.com/douglasdowning
New postings will resume on April 3.
douglasadowning 