Accuracy of Pi: Arguing with Dad

[miguel314]

My dad and I got in an argument about accuracy of pi values. He said that the ratio 22/7 will always be more accurate than any decimal value of pi. I said that the value 3.14159265358979 is much more accurate. I'm 100% certain that I am correct, but I can't really think of how to prove this to him. I'd also like to know how those values are measured, exactly. Thank you for your time.

 

[chroot]

22/7 is an approximation to pi. It's not even accurate to three digits.

- Warren

 

[chroot]

Everything you ever wanted to know about pi:

http://www.mathforum.org/dr.math/faq/faq.pi.html

- Warren

 

[HallsofIvy]

22/7= 3.142857143. As chroot said, not even to three digits.

(It is, however, the best approximate fraction with no more than 2 digits in the numerator.)

 

[Zorodius]

To actually answer your question, you are looking for a proof of the irrationality of Pi. One such proof is http://www.lrz-muenchen.de/~hr/numb/pi-irr.html Google for "irrational pi proof" to see more.

Of course, in this context, the best "proof" would probably be to show him a calculator, press the Pi key, and then enter 22/7 for contrast.

 

[miguel314]

thanks for the help, all...

 

[robert Ihnot]

The value for pi of 335/113 = 3.14159292 is accurate to six decimals, the last two digits should be 65--and it is easy to remember. For a list of these continued fractions see: http://mathworld.wolfram.com/PiContinuedFraction.html