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Posted by dow on July 12, 2010, 4:43 am

My machine comes up with r = 2.718683324663133. However, the final few
digits are pretty well bound to be wrong, and I wouldn't really trust
any after the "4". There are bound to be errors building in from the
right-hand end, and the more iterations that are done around the loop,
the further to the left these errors will creep. Increasing precision
from the left will eventually meet increasing error from the right.
(This is beginning to sound political.)

But ten significant digits is something like measuring the
circumference of the earth to the nearest centimetre. Probably good
enough for most practical purposes.


Posted by Morris Dovey on July 12, 2010, 1:21 pm
On 7/11/2010 11:43 PM, dow wrote:

Agreed, although the creep can be (somewhat) improved upon by avoiding
the cumulative error resulting from an inexact representation for dx...

    for (i=0; i<=n; i=i+1)
    {  x = xLeft + (i * (xRight - xLeft)) / n;
       y = f(x);

Probably. :)

At some point accuracy buffs should be taking temperature, humidity,
atmospheric pressure, and gravity into account. I did once work on a
testing machine that would pause to auto-recalibrate if a human (heat
source) approached within ~2.5m

_Very_ old joke: Calculate to ten decimal places, measure with a
yardstick, mark with a crayon, cut with an axe, and hammer into place.

Morris Dovey

Posted by daestrom on July 12, 2010, 9:50 pm
 Morris Dovey wrote:

I like the old joke.

Like the difference between an engineer and a mathematician.  Both are
placed on one side of the room and a voluptuous naked women is placed on
the other.  They are told that they can only halve the distance
remaining to the women every 15 minutes.

The mathematician says, "Well, if I can only halve the remaining
distance, I'll never actually reach her, so I give up."

The engineer, moves halve the distance.  Fifteen minutes later he halves
  the remaining distance.  Over the next thirty minutes he halves the
distance two more times.  Then he reaches out and grabs the women and
says, "Close ENOUGH!!!"


Posted by dow on July 13, 2010, 1:10 am
Maybe the mathematician doesn't like voluptuous women...

Posted by Morris Dovey on July 13, 2010, 2:28 am
 On 7/12/2010 8:10 PM, dow wrote:

Methinks the mathematician would validate the unstated hypothesis by
inviting her to meet him halfway. :)

Morris Dovey

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