Driver to drive?

[Michael A. Terrell]

Spehro Pefhany wrote:

What did you guys call these things? Or do you recognize them)

http://news.thomasnet.com/images/large/521/521350.jpg
http://www.bradleycorp.com/images/products/fixtures/wf2808_highres.jpg

We had those in the metalshop and woodshops in Jr. High & high
school. The called them 'institutional sinks'.

--
You can't have a sense of humor, if you have no sense!

 

[James Arthur]

Tim Williams wrote:

Come to think of it, I have a few IR2101s that I could just run at 0V as
dual drivers for my immediate goal. That might work out. Still not an
ideal solution, a weak dual TC4420 is really what I want, but I happen to
have some of these on hand.

Tim

A series resistor 'weakens' the best of 'em.

James Arthur

 

[John Larkin]

On Mon, 15 Jun 2009 11:57:26 -0700, Joerg
<notthisjoergsch@removethispacbell.net> wrote:

John Larkin wrote:
On Sun, 14 Jun 2009 20:58:29 -0500, "Tim Williams"
tmoranwms@charter.net> wrote:

I've tried various methods over the years to drive gate drive transformers
with a positive-zero-negative-zero waveform. None of them are very good...

For instance, I did this oh about 4 years ago:
http://webpages.charter.net/dawill/Images/H%20Bridge%20Transformer%20Driver%202.gif
Simple, but needs bipolar supplies.
About 2 years ago:
http://webpages.charter.net/dawill/Images/H%20Bridge%20Transformer%20Driver.gif
Good performance when the snubber's current is continuous. Tedious.
This morning:
http://webpages.charter.net/dawill/Images/H%20Bridge%20Transformer%20Driver%203.gif
(A and B are open collector outputs.) Current sources stabilize output
fairly well, but double followers make sucky offset when current reverses
(~2.4V!).

The common problem in all three is getting a TL494 or etc. to drive MOSFETs.
It'd be so much nicer if they had a complementary bipolar, or better yet
FET, output (ala SG3525 (almost) or UC3842).

What do you do to drive a GDT?

Tim

It's often easier to use a logic level coupler and float a real gate
driver chip on the fet source. No duty cycle problems, no leakage
inductance, standard parts. DC/DC converters are cheap nowadays.


But careful, some might not like flying up and down with the source if
those transitions are fast and the amplitudes are highish. Other
solution: Oscillator, li'l transformer, rectify output, use device up
there that doesn't need a precisely regulated supply voltage.

One weird thing we've done to get floating power is to use a
diode-capacitor thing that gets recharged every time the source swings
to ground, plus a paralleled, very weak photovoltaic optocoupler to
hold it up at DC.

John

 

[Joerg]

John Larkin wrote:

On Tue, 16 Jun 2009 12:56:06 -0700, "RST Engineering - JIm"
jweir43@gmail.com> wrote:

Jan Crystals, Ft. Myers FL. Google for the web page.

Jim
WX6RST


"Joerg" <notthisjoergsch@removethispacbell.net> wrote in message
news:tOzZl.20427$D32.4813@flpi146.ffdc.sbc.com...


Back in the day, you used to be able to get specific crystal frequencies
reasonably inexpensively in small quantities--can you still?

Yes. Best to ask a ham radio operator who still builds stuff (before they
are extinct ...) for some good hints where to buy.

This

ftp://jjlarkin.lmi.net/Lap-Tech.JPG

is a 40 MHz oven-type vacuum-sealed glass AT-cut crystal that is made
for us by Lap-Tech in Ontario. They mark the turning-point temperature
on each one. These are superb crystals... high Q, low aging. They look
like little pieces of jewelry.

I've got some 1-1/2" long glass ones in the 100kHz range here that look
very posh. And yeah, they were also sinfully expensive.

--
Regards, Joerg

http://www.analogconsultants.com/

"gmail" domain blocked because of excessive spam.
Use another domain or send PM.

 

[John Larkin]

On Wed, 17 Jun 2009 12:05:37 -0700, Joerg
<notthisjoergsch@removethispacbell.net> wrote:

John Larkin wrote:
On Tue, 16 Jun 2009 12:56:06 -0700, "RST Engineering - JIm"
jweir43@gmail.com> wrote:

Jan Crystals, Ft. Myers FL. Google for the web page.

Jim
WX6RST


"Joerg" <notthisjoergsch@removethispacbell.net> wrote in message
news:tOzZl.20427$D32.4813@flpi146.ffdc.sbc.com...


Back in the day, you used to be able to get specific crystal frequencies
reasonably inexpensively in small quantities--can you still?

Yes. Best to ask a ham radio operator who still builds stuff (before they
are extinct ...) for some good hints where to buy.

This

ftp://jjlarkin.lmi.net/Lap-Tech.JPG

is a 40 MHz oven-type vacuum-sealed glass AT-cut crystal that is made
for us by Lap-Tech in Ontario. They mark the turning-point temperature
on each one. These are superb crystals... high Q, low aging. They look
like little pieces of jewelry.


I've got some 1-1/2" long glass ones in the 100kHz range here that look
very posh. And yeah, they were also sinfully expensive.

These are about $12.

John

 

[Rich Grise]

On Tue, 16 Jun 2009 22:36:42 -0400, Spehro Pefhany wrote:

http://news.thomasnet.com/images/large/521/521350.jpg
http://www.bradleycorp.com/images/products/fixtures/wf2808_highres.jpg

Hand sink?

Cheers!
Rich

 

[Ben Bradley]

On Sat, 09 May 2009 18:34:11 -0700, Jim Thompson
<To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

I'm using Agent v5. It's really simple to set up filters...

I've been using Free Agent since it came on my Mindspring CD last
millenium, and I suppose this is the excuse I need to actually pay for
the real version.

Primarily you delete anything from googlegroups, gmail and yahoo, BUT
precede that filter with a whitelist (easier than it sounds, I have
only 42 individuals in my whitelist

Is there anything more specific you can share about your filters?

Then, of course, there's specialty filters for NymNuts, Slowman and
Eeyore, but those are trivial to do, also.

Lately there also seems to be "something wrong," so I need to set
up my precious filters.

The tricky part is getting rid of the troll-feeders who keep NymNuts,
Slowman and Eeyore riled up. I do that with a macro (Macro Express
required).

...Jim Thompson

 

[Jim Thompson]

On Thu, 18 Jun 2009 14:15:36 -0400, Ben Bradley
<ben_u_bradley@etcmail.com> wrote:

On Sat, 09 May 2009 18:34:11 -0700, Jim Thompson
To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

I'm using Agent v5. It's really simple to set up filters...

I've been using Free Agent since it came on my Mindspring CD last
millenium, and I suppose this is the excuse I need to actually pay for
the real version.


Primarily you delete anything from googlegroups, gmail and yahoo, BUT
precede that filter with a whitelist (easier than it sounds, I have
only 42 individuals in my whitelist

Is there anything more specific you can share about your filters?

Is your E-mail address valid? If so I'll E-mail my filters to you.

Then, of course, there's specialty filters for NymNuts, Slowman and
Eeyore, but those are trivial to do, also.

Lately there also seems to be "something wrong," so I need to set
up my precious filters.


The tricky part is getting rid of the troll-feeders who keep NymNuts,
Slowman and Eeyore riled up. I do that with a macro (Macro Express
required).

...Jim Thompson

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

Isn't the definition of "totalitarian" when the government owns
significant manufacturing; and controls the major media outlets?

 

[Baron]

Jim Thompson wrote:

On Thu, 18 Jun 2009 14:15:36 -0400, Ben Bradley
ben_u_bradley@etcmail.com> wrote:

On Sat, 09 May 2009 18:34:11 -0700, Jim Thompson
To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

I'm using Agent v5. It's really simple to set up filters...

I've been using Free Agent since it came on my Mindspring CD last
millenium, and I suppose this is the excuse I need to actually pay for
the real version.


Primarily you delete anything from googlegroups, gmail and yahoo, BUT
precede that filter with a whitelist (easier than it sounds, I have
only 42 individuals in my whitelist

Is there anything more specific you can share about your filters?

Is your E-mail address valid? If so I'll E-mail my filters to you.


Then, of course, there's specialty filters for NymNuts, Slowman and
Eeyore, but those are trivial to do, also.

Lately there also seems to be "something wrong," so I need to set
up my precious filters.


The tricky part is getting rid of the troll-feeders who keep NymNuts,
Slowman and Eeyore riled up. I do that with a macro (Macro Express
required).

...Jim Thompson

...Jim Thompson

I don't use "Agent" but using data from Jim's filter rules allowed me to
improve mine. I see a lot less of the rubbish now. Except when
someone replies to a filtered string.

I don't remember if I said thanks to Jim !
Either way Thanks.

--
Best Regards:
Baron.

 

[Joerg]

Baron wrote:

Jim Thompson wrote:

On Thu, 18 Jun 2009 14:15:36 -0400, Ben Bradley
ben_u_bradley@etcmail.com> wrote:

On Sat, 09 May 2009 18:34:11 -0700, Jim Thompson
To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

I'm using Agent v5. It's really simple to set up filters...
I've been using Free Agent since it came on my Mindspring CD last
millenium, and I suppose this is the excuse I need to actually pay for
the real version.

Primarily you delete anything from googlegroups, gmail and yahoo, BUT
precede that filter with a whitelist (easier than it sounds, I have
only 42 individuals in my whitelist
Is there anything more specific you can share about your filters?
Is your E-mail address valid? If so I'll E-mail my filters to you.

Then, of course, there's specialty filters for NymNuts, Slowman and
Eeyore, but those are trivial to do, also.
Lately there also seems to be "something wrong," so I need to set
up my precious filters.

The tricky part is getting rid of the troll-feeders who keep NymNuts,
Slowman and Eeyore riled up. I do that with a macro (Macro Express
required).

...Jim Thompson
...Jim Thompson

I don't use "Agent" but using data from Jim's filter rules allowed me to
improve mine. I see a lot less of the rubbish now. Except when
someone replies to a filtered string.

I don't remember if I said thanks to Jim !
Either way Thanks.

I simply deep-sixed anything google and, voila, I see no rubbish any
more. Other NGs have the occasional Rolex or Gucci offer but even there
that dropped from obnoxious to a mere trickle. This was surprisingly simple.

Needless to say that when my ISP announced they'll drop Usenet I did
_not_ consider using google groups. Not for one millisecond.

--
Regards, Joerg

http://www.analogconsultants.com/

"gmail" domain blocked because of excessive spam.
Use another domain or send PM.

 

[Jim Thompson]

On Thu, 18 Jun 2009 20:54:03 +0100, Baron
<baron.nospam@linuxmaniac.nospam.net> wrote:

Jim Thompson wrote:

On Thu, 18 Jun 2009 14:15:36 -0400, Ben Bradley
ben_u_bradley@etcmail.com> wrote:

On Sat, 09 May 2009 18:34:11 -0700, Jim Thompson
To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

I'm using Agent v5. It's really simple to set up filters...

I've been using Free Agent since it came on my Mindspring CD last
millenium, and I suppose this is the excuse I need to actually pay for
the real version.


Primarily you delete anything from googlegroups, gmail and yahoo, BUT
precede that filter with a whitelist (easier than it sounds, I have
only 42 individuals in my whitelist

Is there anything more specific you can share about your filters?

Is your E-mail address valid? If so I'll E-mail my filters to you.


Then, of course, there's specialty filters for NymNuts, Slowman and
Eeyore, but those are trivial to do, also.

Lately there also seems to be "something wrong," so I need to set
up my precious filters.


The tricky part is getting rid of the troll-feeders who keep NymNuts,
Slowman and Eeyore riled up. I do that with a macro (Macro Express
required).

...Jim Thompson

...Jim Thompson

I don't use "Agent" but using data from Jim's filter rules allowed me to
improve mine. I see a lot less of the rubbish now. Except when
someone replies to a filtered string.

That's why I keep annoying Agent support... add "References:"
filtering, then bye-bye troll feeders.

I don't remember if I said thanks to Jim !
Either way Thanks.

You are quite welcome!

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

Isn't the definition of "totalitarian" when the government owns
significant manufacturing; and controls the major media outlets?

 

[Jim Thompson]

On Thu, 18 Jun 2009 13:27:38 -0700, Joerg <invalid@invalid.invalid>
wrote:

[snip]

I simply deep-sixed anything google and, voila, I see no rubbish any
more.

Only problem with that is the 37+ "good guys" posting from
googlegroups. That's why my filters whitelist _first_, then kill
googlegroups.

Other NGs have the occasional Rolex or Gucci offer but even there
that dropped from obnoxious to a mere trickle. This was surprisingly simple.

Needless to say that when my ISP announced they'll drop Usenet I did
_not_ consider using google groups. Not for one millisecond.

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

Isn't the definition of "totalitarian" when the government owns
significant manufacturing; and controls the major media outlets?

 

[Joerg]

Jim Thompson wrote:

On Thu, 18 Jun 2009 13:27:38 -0700, Joerg <invalid@invalid.invalid
wrote:

[snip]
I simply deep-sixed anything google and, voila, I see no rubbish any
more.

Only problem with that is the 37+ "good guys" posting from
googlegroups. That's why my filters whitelist _first_, then kill
googlegroups.

Maybe they should get _real_ Usenet? I mean, it ain't that hard. My ISP
will terminate the service in three weeks so I just got myself a nice
new Usenet service. Costs a whopping 10 Euros per year. Posting from
there right now (news.individual.de). Customer service is excellent. My
payment seemed stuck over there or somewhere, wrote email, went to
kitchen to get coffee, came back, had a personal response saying that
the money wasn't there yet but that they turned on my account on good
faith. At 7:30pm local time. Now that's what I call service.

[...]

--
Regards, Joerg

http://www.analogconsultants.com/

"gmail" domain blocked because of excessive spam.
Use another domain or send PM.

 

[Ben Bradley]

On Thu, 18 Jun 2009 11:36:14 -0700, Jim Thompson
<To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

On Thu, 18 Jun 2009 14:15:36 -0400, Ben Bradley
ben_u_bradley@etcmail.com> wrote:

On Sat, 09 May 2009 18:34:11 -0700, Jim Thompson
To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

I'm using Agent v5. It's really simple to set up filters...

I've been using Free Agent since it came on my Mindspring CD last
millenium, and I suppose this is the excuse I need to actually pay for
the real version.


Primarily you delete anything from googlegroups, gmail and yahoo, BUT
precede that filter with a whitelist (easier than it sounds, I have
only 42 individuals in my whitelist

Is there anything more specific you can share about your filters?

Is your E-mail address valid? If so I'll E-mail my filters to you.

Yes it is, I only use the address for Usenet posting and I'm amazed
I only get a few spams a week to it.

I'll be looking for your email!

 

[Jon Kirwan]

On Tue, 16 Jun 2009 12:24:36 -0700, I wrote:

snip
The code "says:"

1: m=0; ' P(-2)
2: n=1; ' P(-1)
3: c=1; ' Q(-2)
4: d=0; ' Q(-1)
5: for (i=0;i<15;++i) { ' Perform a loop until useful digits expire
6: k = trunc(t) ' generate a
7: if (k>10^10) break;
8: v=m; ' P(n-2)= P(n-1)
9: m=n; ' P(n-1)= P
10: n=v+k*n; ' P = P(n-2) + a * P(n-1)
11: v=c; ' Q(n-2)= Q(n-1)
12: c=d; ' Q(n-1)= Q
13: d=v+k*d; ' Q = Q(n-2) + a * Q(n-1)
14: print n,"/",d,"\t",n/d-h,"\n";
15: t=1/(t-k) ' next iteration with t=1/(t-a)
16: }
snip

I added a short DOS program (yes, it runs under WinXP and doesn't tie
up the processor, when running -- it uses the multiplex interrupt to
pass back unneeded CPU time to Windows) to display the convergents of
continued fraction values. It includes a calculator feature and
displays floating point notation, as well. Kind of a swiss army knife
thing.

http://www.infinitefactors.org/math/cf.zip
http://www.infinitefactors.org/math/cf.exe

The ZIP simply contains the DOS exe file.

It shouldn't be too hard to use. But you'll need the DOS box. It
will run on DOS-only systems and old Windows stuff, as well. Just a
QB program. It's free to have, pass around, etc. If anyone wants the
code, that's free, too. Just ask. It's a zero-order attempt, but
seems to work modestly well.

Jon

 

[JosephKK]

On Thu, 18 Jun 2009 14:57:29 -0700, Jim Thompson
<To-Email-Use-The-Envelope-Icon@My-Web-Site.com> wrote:

On Thu, 18 Jun 2009 13:27:38 -0700, Joerg <invalid@invalid.invalid
wrote:

[snip]

I simply deep-sixed anything google and, voila, I see no rubbish any
more.

Only problem with that is the 37+ "good guys" posting from
googlegroups. That's why my filters whitelist _first_, then kill
googlegroups.

Other NGs have the occasional Rolex or Gucci offer but even there
that dropped from obnoxious to a mere trickle. This was surprisingly simple.

Needless to say that when my ISP announced they'll drop Usenet I did
_not_ consider using google groups. Not for one millisecond.

...Jim Thompson

If it is strictly internal to agent 5 i am interested.

 

[The Phantom]

On Tue, 16 Jun 2009 00:35:41 -0500, James Waldby <no@no.no> wrote:

Anyway, the general idea of continued-fraction rational-approximation
for some fraction h is to repeatedly find an integer that accounts
for most of the difference between h and the previous convergent.
That integer is the integer part of 1/t, where t is the fractional
part of the previous value of t. The variables c and m in the
programs are used to keep track of previous n and d values for
computing values of successive convergents, per Theorem 1 which
justifies the calculations, although it doesn't make them obvious.

Here's an example with h=3.4567, where the program's numeric output is:
n/d k t h - n/d
3/1 3 0.4567000000000 0.4567000000000
7/2 2 0.1896211955332 -0.0433000000000
38/11 5 0.2736720554273 0.0021545454545
121/35 3 0.6540084388183 -0.0004428571429
159/46 1 0.5290322580651 0.0001782608696
280/81 1 0.8902439024371 -0.0000901234568
439/127 1 0.1232876712354 0.0000070866142
3792/1097 8 0.1111111109480 -0.0000000911577
34567/10000 9 0.0000000132091 0.0000000000000

This means that the continued fraction for h= 3.4567 is
[3; 2, 5, 3, 1, 1, 1, 8, 9], (from the k column) which stands for
3 + 1/(2 + 1/(5 + 1/(3 + 1/(1 + 1/(1 + 1/(1 + 1/(8 + 1/9)))))))

The first convergent is 3, which is 0.4567 too small;
second, 3 + 1/(2) = 7/2, which is 0.0433 too big;
third, 3 + 1/(2 + 1/5) = 38/11, which is 0.00215... too small;
fourth, 3 + 1/(2 + 1/(5 + 1/(3))) = 121/35, etc, with signs
of h - n/d alternating per Theorem 3 of wikipedia page.

When the program computes 121/35 after 7/2 and 38/11, it has
m=7, n=38, c=2, d=11, and k=3. 121/35 = (7+3*38) / (2+3*11).

You missed 24/7 and 31/9 between 7/2 and 38/11. On the Wikipedia page, read the
part about "semiconvergents", and the following "Best Rational Approximations".

CBFalconer's brute force program in the "Continued Fraction Program" thread
finds them, but using semiconvergents will get them in a more elegant fashion.

 

[John Larkin]

On 25 Jun 2009 11:51:01 -0500, The Phantom <phantom@aol.com> wrote:

On Tue, 16 Jun 2009 00:35:41 -0500, James Waldby <no@no.no> wrote:



Anyway, the general idea of continued-fraction rational-approximation
for some fraction h is to repeatedly find an integer that accounts
for most of the difference between h and the previous convergent.
That integer is the integer part of 1/t, where t is the fractional
part of the previous value of t. The variables c and m in the
programs are used to keep track of previous n and d values for
computing values of successive convergents, per Theorem 1 which
justifies the calculations, although it doesn't make them obvious.

Here's an example with h=3.4567, where the program's numeric output is:
n/d k t h - n/d
3/1 3 0.4567000000000 0.4567000000000
7/2 2 0.1896211955332 -0.0433000000000
38/11 5 0.2736720554273 0.0021545454545
121/35 3 0.6540084388183 -0.0004428571429
159/46 1 0.5290322580651 0.0001782608696
280/81 1 0.8902439024371 -0.0000901234568
439/127 1 0.1232876712354 0.0000070866142
3792/1097 8 0.1111111109480 -0.0000000911577
34567/10000 9 0.0000000132091 0.0000000000000

This means that the continued fraction for h= 3.4567 is
[3; 2, 5, 3, 1, 1, 1, 8, 9], (from the k column) which stands for
3 + 1/(2 + 1/(5 + 1/(3 + 1/(1 + 1/(1 + 1/(1 + 1/(8 + 1/9)))))))

The first convergent is 3, which is 0.4567 too small;
second, 3 + 1/(2) = 7/2, which is 0.0433 too big;
third, 3 + 1/(2 + 1/5) = 38/11, which is 0.00215... too small;
fourth, 3 + 1/(2 + 1/(5 + 1/(3))) = 121/35, etc, with signs
of h - n/d alternating per Theorem 3 of wikipedia page.

When the program computes 121/35 after 7/2 and 38/11, it has
m=7, n=38, c=2, d=11, and k=3. 121/35 = (7+3*38) / (2+3*11).

You missed 24/7 and 31/9 between 7/2 and 38/11. On the Wikipedia page, read the
part about "semiconvergents", and the following "Best Rational Approximations".

CBFalconer's brute force program in the "Continued Fraction Program" thread
finds them, but using semiconvergents will get them in a more elegant fashion.

How about starting with 1/1 and looping on...

if the fraction is below the target, bump the numerator

if above, bump the denominator

Wouldn't that work? A PC could do some decent fraction of a billion
iterations per second. Who needs elegance these days?

John

 

[Jon Kirwan]

On Thu, 25 Jun 2009 12:22:44 -0700, John Larkin
<jjlarkin@highNOTlandTHIStechnologyPART.com> wrote:

On 25 Jun 2009 11:51:01 -0500, The Phantom <phantom@aol.com> wrote:

On Tue, 16 Jun 2009 00:35:41 -0500, James Waldby <no@no.no> wrote:

Anyway, the general idea of continued-fraction rational-approximation
for some fraction h is to repeatedly find an integer that accounts
for most of the difference between h and the previous convergent.
That integer is the integer part of 1/t, where t is the fractional
part of the previous value of t. The variables c and m in the
programs are used to keep track of previous n and d values for
computing values of successive convergents, per Theorem 1 which
justifies the calculations, although it doesn't make them obvious.

Here's an example with h=3.4567, where the program's numeric output is:
n/d k t h - n/d
3/1 3 0.4567000000000 0.4567000000000
7/2 2 0.1896211955332 -0.0433000000000
38/11 5 0.2736720554273 0.0021545454545
121/35 3 0.6540084388183 -0.0004428571429
159/46 1 0.5290322580651 0.0001782608696
280/81 1 0.8902439024371 -0.0000901234568
439/127 1 0.1232876712354 0.0000070866142
3792/1097 8 0.1111111109480 -0.0000000911577
34567/10000 9 0.0000000132091 0.0000000000000

This means that the continued fraction for h= 3.4567 is
[3; 2, 5, 3, 1, 1, 1, 8, 9], (from the k column) which stands for
3 + 1/(2 + 1/(5 + 1/(3 + 1/(1 + 1/(1 + 1/(1 + 1/(8 + 1/9)))))))

The first convergent is 3, which is 0.4567 too small;
second, 3 + 1/(2) = 7/2, which is 0.0433 too big;
third, 3 + 1/(2 + 1/5) = 38/11, which is 0.00215... too small;
fourth, 3 + 1/(2 + 1/(5 + 1/(3))) = 121/35, etc, with signs
of h - n/d alternating per Theorem 3 of wikipedia page.

When the program computes 121/35 after 7/2 and 38/11, it has
m=7, n=38, c=2, d=11, and k=3. 121/35 = (7+3*38) / (2+3*11).

You missed 24/7 and 31/9 between 7/2 and 38/11. On the Wikipedia page, read the
part about "semiconvergents", and the following "Best Rational Approximations".

CBFalconer's brute force program in the "Continued Fraction Program" thread
finds them, but using semiconvergents will get them in a more elegant fashion.

How about starting with 1/1 and looping on...

if the fraction is below the target, bump the numerator

if above, bump the denominator

Wouldn't that work? A PC could do some decent fraction of a billion
iterations per second. Who needs elegance these days?

I think that's a point in the American Scientist article posted by The
Phantom under a different thread:

http://www.americanscientist.org/issues/pub/on-the-teeth-of-wheels/5

The author summarizes at the end, this way:

"The fact is, the design of simple gear trains is no longer a
computationally interesting problem, because computation itself has
overwhelmed it. With so much calculating power at your fingertips,
it's hardly worth the bother of being clever. You can solve gearing
problems by brute-force, using methods that would have been
unthinkable for Camus or Brocot, or even for Merritt, who was writing
hardly more than 50 years ago. If you need to approximate some ratio,
just have the computer try all pairs of gears with no more than 100
teeth. There are only 10,000 combinations; you can churn them out in
an instant. For a two-stage compound train, running through the 100
million possibilities is a labor of minutes."

"The whirling gears of progress have put the gearmakers out of work."

Jon

 

[The Phantom]

On Thu, 25 Jun 2009 12:22:44 -0700, John Larkin
<jjlarkin@highNOTlandTHIStechnologyPART.com> wrote:

How about starting with 1/1 and looping on...

if the fraction is below the target, bump the numerator

if above, bump the denominator

Wouldn't that work? A PC could do some decent fraction of a billion
iterations per second. Who needs elegance these days?

John

That's what CBFalconer's brute force program does. For finding fractions with

the small numerators and denominators this thread has been discussing, and using
a modern computer, brute force is just fine.

However, when doing the computations on a slow machine, such as a pocket
calculator, continued fraction methods may be enough faster to make the
difference between a boring wait and immediate answers.

Elegance is its own reward.