Hi Dana,

while studying Fourier Analysis.
I was fascinated with Fourier Transforms also, but that was in the late
50's when I was in college [Queens College, New York City], before I ever
heard of electronic computers.

http://documents.wolfram.com/mathema...ulatingPi.html
Thanks for the link. I love the articles. I often thought of buying
Mathematica's package, but didn't because I dropped out of math after
quitting graduate school because computer programming was much more
exciting. I only do math with my grandchildren now.

BTW, are there any open-source/freeware packages on the 'Net for writing
mathematical expressions? I'm using MS Word's Drawing toolbar for
documenting for my grandson what we did the other day (to allow him to
review it when working on future problems.)

Pi = (2^n) * S(2 - S(2+S(2+...))),

Although this in not the same equation, here's a very similar equation.
(Vieta's equation from above link)

Although Vieta's equation is very neat, it's my guess that his work is not
very well known. I fell in love with math as a grammar school sophmore, when
a teacher gave me a book on algebra (probably to keep me from interrupting
her in math lectures.) But I fell deeply in love when I discovered Number
Theory as a member of the math team in high school. Euler and Gauss were my
heros.

My equation met my goal of being understandable by an elementary school kid
without any mathematical training beyond elementary algebra.

I was impressed (but not surprised) that Archimedes used essentially the
same appoach to compute ? as the ratio of the areas of the unit circle and
unit rectangle. That I used a sinilar approach only proves I had a good
education.

Sub Pi_Vietas_Formula()

Thanks for the encoding of Vieta's formula as an Excel subroutine. I'll run
it and show it to my grandson when I compare it to my formula as we jack up
the precision and number of iterations. When we run it on his (older and
slower) machine, we should find a perceptible performance difference.

Best wishes,
Richard Muller