[Tutor] A better way to estimate the value of Pi?

[Dave Angel]

On 10/17/2011 11:55 AM, Sagar Shankar wrote:
>
>> The "real" value of 4/3.0  is 1 followed by an unending number of 3's.
>>
>> Each successive fraction's floating point value will be "off" by some
>> relatively small value. Those errors will probably add up.
>>
>> Another limitation of floating point numbers is that there is a maximum and
>> a minimum exponent. Eventually the fractions will be too small to convert to
>> float, raising an overflow exception.
>>
>> Allof this raises the question - what computer algorithms successively
>> approximate pi exactly?
>>
>> --
>> Bob Gailer
>> 919-636-4239
>> Chapel Hill NC
>>
>>

There are two separate problems with doing this operation in floats.  
One is that the final answer can be no closer than a float knows how to 
represent.  But the second is the cumulative error caused by adding a 
bunch of values of differing magnitudes.

You can at least reduce the second by adding them in reverse order. In 
other words, build a list of floats for the terms of the series, then 
reverse the list and sum it.

-- 

DaveA