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

*> With a tweak to the output format specification (%G -> %12.10f) the code*

*> produces*

*> Focal length: 1.0000000000*

*> Depth of dish: 1.8478097550*

*> Radius of rim: 2.7186833247*

*> Angular radius of rim, seen from focus 72.6801340944 degrees*

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.

dow

Posted by *Morris Dovey* on July 12, 2010, 1:21 pm

On 7/11/2010 11:43 PM, dow wrote:

*> 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.)*

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);

...

}

*> But ten significant digits is something like measuring the*

*> circumference of the earth to the nearest centimetre. Probably good*

*> enough for most practical purposes.*

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

http://www.iedu.com/DeSoto/

Posted by *daestrom* on July 12, 2010, 9:50 pm

Morris Dovey wrote:

*> On 7/11/2010 11:43 PM, dow wrote:*

*> *

*>> 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.)*

*> *

*> 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);*

*> ...*

*> }*

*> *

*>> But ten significant digits is something like measuring the*

*>> circumference of the earth to the nearest centimetre. Probably good*

*>> enough for most practical purposes.*

*> *

*> 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.*

*> *

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!!!"

daestrom

Posted by *dow* on July 13, 2010, 1:10 am

*> Morris Dovey wrote:*

*> > On 7/11/2010 11:43 PM, dow wrote:*

*> >> 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.)*

*> > 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);*

*> > ...*

*> > }*

*> >> But ten significant digits is something like measuring the*

*> >> circumference of the earth to the nearest centimetre. Probably good*

*> >> enough for most practical purposes.*

*> > 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.*

*> 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!!!"*

*> daestrom- Hide quoted text -*

*> - Show quoted text -*

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:

*> Maybe the mathematician doesn't like voluptuous women...*

Methinks the mathematician would validate the unstated hypothesis by

inviting her to meet him halfway. :)

--

Morris Dovey

http://www.iedu.com/DeSoto/

> With a tweak to the output format specification (%G -> %12.10f) the code> produces> Focal length: 1.0000000000> Depth of dish: 1.8478097550> Radius of rim: 2.7186833247> Angular radius of rim, seen from focus 72.6801340944 degrees