On 2004 Apr 17 , at 12:04 AM, Brij Bhushan Vij wrote:
provided ... Pi are DEFINED'.
This can be done by a glance at my worked values for Pi used by man, Refer:
http://the-light.com/bbv_pi-radian.jpg
One can DETERMINE pi, but one cannot DEFINE pi in the sense that SI defines the metre and the second etc. Pi is a given factor of the universe we live in. It is the value that it is; we don't have the ability to "define" it to be any other value. It can be determined to any number of decimal places (but it takes a LONG time to get those very small decimal places). Pi is exact to an infinite number of decimal places but we can never calculate all of them because it would take an infinite amount of time to calculate an infinite number of decimal places. (Also, no one could use the results because it would take an infinite amount of time to use a number with an infinite number of decimal places.)
You can say "Pi is defined as the ratio of the circumference to the diameter of a circle" but that does not define the value of pi as it merely tells how to go about measuring it. There are mathematical relations between the geometry of a circle and other known, fixed constants which provide methods by which purely calculated values of pi can be found, rather than finding it by dividing two measured values (circumference and diameter). Those purely calculated values give values which can be more precise than any possible measurement.
By the way, Brij, I tried to refer to the web page mentioned in the last line of your message and I received the error message:
File Not Found The requested URL was not found on this server.
Regards, Bill Hooper Fernandina Beach, Florida, USA <><><><><><><><><><><><> Make it simple; Make it Metric <><><><><><><><><><><><>
