The resistor cube problem

"Jim Thompson" <thegreatone@example.com> schreef in bericht
news:eek:v88b01gl7fpv2qdbh382tuumgu7hdl48c@4ax.com...
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

On Tue, 25 May 2004 21:21:56 GMT, analog wrote:

Frank Bemelman wrote:
Jim Thompson wrote:
Richard Henry wrote:
Chris Carlen wrote:
[snip]

Unless I'm missing something I count only 11 faces... a dodecahedron
has *12* faces, each of which is a pentagon. I know it quite well
because one of my drafting assignments (when I was in Junior High
School) was to draw a dodecahedron at various rotations.

The 'outline' of the drawing is a face too. 12 faces total.

Ha, it's a stretch of the imagination to get there, but of course you
are quite correct. You win today's topological trophy. But now Jim
has lost "face" in a public forum. :( Perhaps a consolation prize is
in order. Might I suggest a fine Klein bottle decanter for the merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.
Click to expand...
Right, besides, how can you loose something that you have lost
a long time ago already.

--
Thanks, Frank.
(remove 'x' and 'invalid' when replying by email)
 
Activ8 wrote:
On Tue, 25 May 2004 07:07:26 GMT, Robert Baer wrote:

The Phantom wrote:

On Mon, 24 May 2004 17:15:07 -0700, Chris Carlen
crobc@BOGUS_FIELD.earthlink.net> wrote:

The Phantom wrote:
On Mon, 24 May 2004 15:22:14 -0700, Chris Carlen
crcarle@BOGUS.sandia.gov> wrote:


Frank Bemelman wrote:

"Chris Carlen" <crcarle@BOGUS.sandia.gov> schreef in bericht
news:c8ta9v0183o@news4.newsguy.com...


Fun problem. Wasn't what I had originally planned for my first hour of
the day.


Your next assignment is the dodecahedron ;)


If you can draw it, I'll solve it.


Consider the infinite plane grid of 1 ohm resistors with nodes on
the coordinates with integer values, such as (1,1), (2,2), (1,2) etc.
None of the resistors is diagonally connected, as between (1,1) and
(2,2). All the horizontally adjacent and vertically adjacent nodes
have a 1 ohm resistor connected.

What is the resistance between the points (1,1) and (1,2)?

Yes, this is another category of interesting resistor problems. Don't
give me any hints. Though I am not sure when I will try it. It has
been in the back of my mind since seeing it here a few times.

What is the resistance between the points (1,1) and (1,2)?

Yes, of course; typos happen, eh?

What is the resistance between the points (1,1) and (2,2)?


Don't you mean some other points?


Good day!

The cube of 1 ohm resistors, a resistor on each edge, whit the
question as to the value of resistance across the internal body diagnal
can be made more interesting:
State at least three completely differnt ways of solving this problem
and give the electrical and/or mathematical reasons for each step if the
solutions.
For extra credit, state how many different ways there are to solve
that problem - with a brief description of each method (so we know you
are not cheating).

1. Connect points of equal potentials, combine resistors in parallel
and series. The reason you can do this is because equipotential
points can be shorted without fouling things up.

2. apply a current source, write the node equations and solve for
the voltage, divide by current to get R. THe reason you can do this
is bacause KCL says you can.

3. put a voltage across the stinkin' thing, write the mesh
equations, solve for I, divide it into V to get R. THe reason is
KVL.

Extra credit: There are infinite ways to solve this because there's
no telling how many monkeys can guess the correct answer, use a VOM
meter, etc., and who's to say whether any two individual monkeys
arrived at their correct guess the same way, with the exact same
neurons firing identically. My proof I that statistically, anything
is possible no matter how unlikely.

--
Best Regards,
Mike
Click to expand...
Ther are *not* an infinite number of ways; and even if one "bends
therules" and allows minor and/or meaningless variations, ther are still
a limited number of ways to solve the problem.

A variant of method number one can be used as the fastest way to solve
the problem.
Mentally force 12 amps (why? there are 12 resistors) into one corner,
and out of the body diagonal corner.
The current at those corners divide equally into thirds; at each
"exit" resistor there are two others, so the current again divides
equally.
So, the two resistor triads are in parallel for 1/3 ohm, and the three
duals are in parallel for 1/2 ohm then parallel those 3 for 1/6 ohm -
for a total of 1/3 + 1/6 + 1/3 or 5/6 ohms.
That is exact, not an approximation that a calculator would produce.
No time-wasting mesh equations, and the "trick" allows one to either
do an E=I*R at each step to calculate a voltage, add them and do a R=E/I
at the end, or "see" how the current divides and do the parallel R
calculation (like i described).
Note that gives two variants of method number one.
 
"Jim Thompson" <thegreatone@example.com> wrote in message
news:eek:v88b01gl7fpv2qdbh382tuumgu7hdl48c@4ax.com...
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

Ha, it's a stretch of the imagination to get there, but of course you
are quite correct. You win today's topological trophy. But now Jim
has lost "face" in a public forum. :( Perhaps a consolation prize is
in order. Might I suggest a fine Klein bottle decanter for the merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.

...Jim Thompson
Click to expand...
hear, hear. Alas plenty of people like that. Me, I try to acknowledge
mistakes, and then try to learn from them. Having done a fair bit of
production engineering, I learned pretty early on that people randomly screw
stuff up, and its up to me as a designer to take that into account - prevent
screw ups where possible (eg different plugs so you cant get it wrong), then
make sure screw-ups are blindingly obvious so they get caught early on, etc.
Besides, mistakes can be quite exciting with power electronics (little dutch
time bomb, tick-tock-boom).

Cheers
Terry
 
Activ8 wrote:
On 24 May 2004 19:12:09 -0500, The Phantom wrote:

On Mon, 24 May 2004 15:22:14 -0700, Chris Carlen
crcarle@BOGUS.sandia.gov> wrote:

Frank Bemelman wrote:
"Chris Carlen" <crcarle@BOGUS.sandia.gov> schreef in bericht
news:c8ta9v0183o@news4.newsguy.com...

Fun problem. Wasn't what I had originally planned for my first hour of
the day.

Your next assignment is the dodecahedron ;)


If you can draw it, I'll solve it.

Consider the infinite plane grid of 1 ohm resistors with nodes on
the coordinates with integer values, such as (1,1), (2,2), (1,2) etc.
None of the resistors is diagonally connected, as between (1,1) and
(2,2). All the horizontally adjacent and vertically adjacent nodes
have a 1 ohm resistor connected.

What is the resistance between the points (1,1) and (1,2)?

What is the resistance between the points (1,1) and (1,2)?

1,1 1,2 1,3
___ ___
+-|___|--+-|___|-+
| | |
.-. .-. .-.
| | A | | B | |
| | | | | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+
| | |
.-. .-. .-.
| | | | | |
| | C | | D | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ 3,3

Taking only mesh A, we get 1 ohm

Connecting mesh D, it's 2 ohms

scap that approach...

ok connect two equal potential points in both meshes A and D (1,2 to
2,1 and 2,3 to 3,2) and you get

2
1,2 ___ 2,3
+-------|___|--------+
| |
| |
.5 | .5 .5 | .5
___ | ___ ___ | ___
1,1 -|___|---+---|___|-----|___|--+--|___|- 3,3
| |
| |
| |
| |
| ___ |
+--------|___|-------+
2

that's 1.5 ohm or 3(.5)

and since a single 4 R mesh (like A only) would be 1 ohm,
(2,2)-(1,1) = 1,1 and (3,3)-(1,1)=2,2 so j=k is 1 or 2 i.e., the
dimension, n

n R
_____
1 1
2 1.5 crap! need one more

nah. skip the subtraction and go with n=j=k

n R
_____
2 1
3 1.5

R = .5n -- a wild first guess which would make the next higher
dimension grid

R = 2

1,1 1,2 1,3
___ ___
+-|___|--+-|___|-+ R +
| | |
.-. .-. .-.
| | A/ | | B | | R
| | | | | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ R +
| | |
.-. .-. .-.
| | | | / | | R
| | C | | D | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ R +
| | |
.-. .-. .-.
| | | | | | /
| | C | | D | | R
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ R + 4,4

er, it's a bit late for me to stare aat this any more to connect 1,4
with 4,1. I'd rather do a mesh or node analysis at this point.
--
Best Regards,
Mike
Click to expand...
Hmm.. not necessarily leading to an answer, but thinking slow and
"out loud"..

1,1 1,2 1,3
___ ___
+-|_a_|--+-|_b_|-+
| | |
.-. .-. .-.
| | A | | B | |
|c| |d| |e|
'-' '-' '-'
| ___ | ___ |
+-|_f_|--+-|_g_|-+
| | |
.-. .-. .-.
| | | | | |
|h| C |j| D |k|
'-' '-' '-'
| ___ | ___ |
+-|_m_|--+-|_n_|-+ 3,3


Taking the idea of adding resistors b+e=p and h+m=q..

1,1 1,2
___ ___
+-|_a_|--+-|_p_|-+
| | |
.-. .-. |
| | A | | |
|c| |d| |
'-' '-' |
| ___ | ___ |
+-|_f_|--+-|_g_|-+
| | |
| .-. .-.
| | | | |
| |j| D |k|
| '-' '-'
| ___ | ___ |
+-|_q_|--+-|_n_|-+ 3,3

Then delta to wye..

1,1 1,2
___ ___
+-|_a_|--+-|_D_|-+
| |
.-. + ------+
| | A .-. .-.
|c| |P| |G|
'-' '-' '-'
| | |
.-. | |
|J| +----+ |
'-' .-. .-. .-.
| |Q| | | | |
| '-' |j| D |k|
+---+ '-' '-'
| ___ | ___ |
+-|_F_|--+-|_n_|-+ 3,3

Well, it is partly simplified; i used capital letters for the
"diagonal" or "corner" or "compliment" resistors (do not know the proper
term); value seems to be 1/3 ohm each.

Someone else can take it from here...
 
On Tue, 25 May 2004 22:00:36 -0700, Jim Thompson wrote:

On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

On Tue, 25 May 2004 21:21:56 GMT, analog wrote:

Frank Bemelman wrote:
Jim Thompson wrote:
Richard Henry wrote:
Chris Carlen wrote:
[snip]

Unless I'm missing something I count only 11 faces... a dodecahedron
has *12* faces, each of which is a pentagon. I know it quite well
because one of my drafting assignments (when I was in Junior High
School) was to draw a dodecahedron at various rotations.

The 'outline' of the drawing is a face too. 12 faces total.

Ha, it's a stretch of the imagination to get there, but of course you
are quite correct. You win today's topological trophy. But now Jim
has lost "face" in a public forum. :( Perhaps a consolation prize is
in order. Might I suggest a fine Klein bottle decanter for the merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.

...Jim Thompson
Click to expand...
And big deal anyway.

1. Dodecahedrons have little to do with EE

I made the same mistake but caught it after hitting send.

2. Every other 2D representation of a dodecahedron I've seen in the
past has been better because text art is limited.
--
Best Regards,
Mike
 
In article <qhq7b0hioako892cidqoqojcugpo1u9rvq@4ax.com>,
budgie <me@privacy.net> wrote:

On Tue, 25 May 2004 13:12:52 GMT, Al <no.spam@here.com> wrote:

In article <oc65b094q78skvn9192itej4odbltf7m3l@4ax.com>,
budgie <me@privacy.net> wrote:

On 24 May 2004 20:11:54 +0100, John Devereux <jd1@devereux.me.uk> wrote:

(snip O/P stuff re 1R cube)

You know that the cube is symmetrical, and the two points a and b are
at opposite corners. So there is no "preferred" route from a to b. The
currents from a to V1, V2 and V3 will be equal by symmetry. Therefore
the voltage drop will be equal too. So the voltages V1,2,3 are
equal. There is therefore no difference between this circuit and one
with V1,2,3 connected together. In which case the 3 resistors
connected to a are in parallel and the resistance is 1/3 ohm.

You can make the identical argument from the "b" end, so another 1/3
ohm appears.

Finally we now have the remaining 6 resistors V3-5, V2-5, V1-4, V1-6,
V2-5, V2-6. But these are all in parallel too since we connected
V1,2,3 and V4,5,6. So we have a final 1/6 of an ohm giving a total of
1/3+1/3+1/6 = 5/6.

John and Mark have put their respective fingers on the elegant solution
approach. Symmetry is the key, and using a current source helps visualise
the
volt drop across each thrid of the mesh.

BTW, we had this as a problem in high school physics. Several of us gave
the
answer "by eye", without resort to pencil/paper. And the slide rule
probably
wouldn't have helped ....

OK, what is the resistance between two points 2.54 centimeters apart in
an infinite conductive sheet with a resistance of 1 ohm/square?

Do I care?
Click to expand...
Yes you should. Check out this web site, for one:

http://www.esdjournal.com/techpapr/ohms.htm

Al

--
There's never enough time to do it right the first time.......
 
On Wed, 26 May 2004 19:07:15 -0700, "Terry Given"
<the_domes@xtra.co.nz> wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:eek:v88b01gl7fpv2qdbh382tuumgu7hdl48c@4ax.com...
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

Ha, it's a stretch of the imagination to get there, but of course you
are quite correct. You win today's topological trophy. But now Jim
has lost "face" in a public forum. :( Perhaps a consolation prize is
in order. Might I suggest a fine Klein bottle decanter for the merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.

...Jim Thompson

hear, hear. Alas plenty of people like that. Me, I try to acknowledge
mistakes, and then try to learn from them. Having done a fair bit of
production engineering, I learned pretty early on that people randomly screw
stuff up, and its up to me as a designer to take that into account - prevent
screw ups where possible (eg different plugs so you cant get it wrong), then
make sure screw-ups are blindingly obvious so they get caught early on, etc.
Besides, mistakes can be quite exciting with power electronics (little dutch
time bomb, tick-tock-boom).

Cheers
Terry
Click to expand...
I've made so many mistakes in my lifetime that I doubt that any of you
will ever catch up ;-)

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.
 
On Wed, 26 May 2004 13:23:38 GMT, Al <no.spam@here.com> wrote:

In article <qhq7b0hioako892cidqoqojcugpo1u9rvq@4ax.com>,
budgie <me@privacy.net> wrote:

On Tue, 25 May 2004 13:12:52 GMT, Al <no.spam@here.com> wrote:

[snip]

OK, what is the resistance between two points 2.54 centimeters apart in
an infinite conductive sheet with a resistance of 1 ohm/square?

Do I care?

Yes you should. Check out this web site, for one:

http://www.esdjournal.com/techpapr/ohms.htm

Al
Click to expand...
I have been using "ohms/square" for 42 years ;-)

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.
 
"Activ8" <reply2group@ndbbm.net> wrote in message
news:131zw22g63jk6.dlg@news.individual.net...
On Tue, 25 May 2004 22:00:36 -0700, Jim Thompson wrote:

On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

On Tue, 25 May 2004 21:21:56 GMT, analog wrote:

Frank Bemelman wrote:
Jim Thompson wrote:
Richard Henry wrote:
Chris Carlen wrote:
[snip]

Unless I'm missing something I count only 11 faces... a dodecahedron
has *12* faces, each of which is a pentagon. I know it quite well
because one of my drafting assignments (when I was in Junior High
School) was to draw a dodecahedron at various rotations.

The 'outline' of the drawing is a face too. 12 faces total.

Ha, it's a stretch of the imagination to get there, but of course you
are quite correct. You win today's topological trophy. But now Jim
has lost "face" in a public forum. :( Perhaps a consolation prize is
in order. Might I suggest a fine Klein bottle decanter for the merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.

...Jim Thompson

And big deal anyway.

1. Dodecahedrons have little to do with EE

I made the same mistake but caught it after hitting send.

2. Every other 2D representation of a dodecahedron I've seen in the
past has been better because text art is limited.
Click to expand...
I started by printing out a 2D flattened dodecahedron from
mathworld.wolfram.com, lettered the vertices, and then converted to
ascii-art.

I also attempted a solution for an icosahedron, but when I sent it I just
got an error message and I could no longer find the source. I do remember
the result. It was easier than the dodecahedron: 1/5 ohm + 1/10 ohm + 1/5
ohm = 1/2 ohm.

Next up: buckyball.

http://mathworld.wolfram.com/TruncatedIcosahedron.html
 
"Jim Thompson" <thegreatone@example.com> wrote in message
news:9v89b0dqqruj3sbv9556f7l516m73bmkal@4ax.com...
On Wed, 26 May 2004 19:07:15 -0700, "Terry Given"
the_domes@xtra.co.nz> wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:eek:v88b01gl7fpv2qdbh382tuumgu7hdl48c@4ax.com...
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

Ha, it's a stretch of the imagination to get there, but of course
you
are quite correct. You win today's topological trophy. But now Jim
has lost "face" in a public forum. :( Perhaps a consolation prize
is
in order. Might I suggest a fine Klein bottle decanter for the
merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.

...Jim Thompson

hear, hear. Alas plenty of people like that. Me, I try to acknowledge
mistakes, and then try to learn from them. Having done a fair bit of
production engineering, I learned pretty early on that people randomly
screw
stuff up, and its up to me as a designer to take that into account -
prevent
screw ups where possible (eg different plugs so you cant get it wrong),
then
make sure screw-ups are blindingly obvious so they get caught early on,
etc.
Besides, mistakes can be quite exciting with power electronics (little
dutch
time bomb, tick-tock-boom).

Cheers
Terry


I've made so many mistakes in my lifetime that I doubt that any of you
will ever catch up ;-)

...Jim Thompson
Click to expand...
I'm not going to let that stop me trying :} I work hard at not making the
same mistake twice. Luckily there are plenty of other mistakes for me to
choose from, so I havent run out yet.

Cheers
Terry
 
"Dave VanHorn" <dvanhorn@cedar.net> wrote in message
news:GNWdnV_OI_SzNindRVn-jw@comcast.com...
Mobius strip?
Click to expand...
To which posting was this a reply?
 
"Terry Given" <the_domes@xtra.co.nz> wrote in message
news:%H1tc.10441$XI4.375699@news.xtra.co.nz...
"Jim Thompson" <thegreatone@example.com> wrote in message
news:9v89b0dqqruj3sbv9556f7l516m73bmkal@4ax.com...
On Wed, 26 May 2004 19:07:15 -0700, "Terry Given"
the_domes@xtra.co.nz> wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:eek:v88b01gl7fpv2qdbh382tuumgu7hdl48c@4ax.com...
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

Ha, it's a stretch of the imagination to get there, but of course
you
are quite correct. You win today's topological trophy. But now
Jim
has lost "face" in a public forum. :( Perhaps a consolation prize
is
in order. Might I suggest a fine Klein bottle decanter for the
merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight to
solve real problems.

...Jim Thompson

hear, hear. Alas plenty of people like that. Me, I try to acknowledge
mistakes, and then try to learn from them. Having done a fair bit of
production engineering, I learned pretty early on that people randomly
screw
stuff up, and its up to me as a designer to take that into account -
prevent
screw ups where possible (eg different plugs so you cant get it wrong),
then
make sure screw-ups are blindingly obvious so they get caught early on,
etc.
Besides, mistakes can be quite exciting with power electronics (little
dutch
time bomb, tick-tock-boom).

Cheers
Terry


I've made so many mistakes in my lifetime that I doubt that any of you
will ever catch up ;-)

...Jim Thompson

I'm not going to let that stop me trying :} I work hard at not making the
same mistake twice. Luckily there are plenty of other mistakes for me to
choose from, so I havent run out yet.
Click to expand...
I must admit that I have, at least once, realized that I had made the same
mistake before. I work hard at not making the same mistake twice again, so
that I will not have to make that admission again.
 
"Richard Henry" <rphenry@home.com> wrote in message
news:ja6tc.35811$PU5.11951@fed1read06...
"Terry Given" <the_domes@xtra.co.nz> wrote in message
news:%H1tc.10441$XI4.375699@news.xtra.co.nz...
"Jim Thompson" <thegreatone@example.com> wrote in message
news:9v89b0dqqruj3sbv9556f7l516m73bmkal@4ax.com...
On Wed, 26 May 2004 19:07:15 -0700, "Terry Given"
the_domes@xtra.co.nz> wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:eek:v88b01gl7fpv2qdbh382tuumgu7hdl48c@4ax.com...
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
wrote:

Ha, it's a stretch of the imagination to get there, but of
course
you
are quite correct. You win today's topological trophy. But now
Jim
has lost "face" in a public forum. :( Perhaps a consolation
prize
is
in order. Might I suggest a fine Klein bottle decanter for the
merlot
(would lead to better concentration and more wine in the food).

Check the time of my post where I corrected myself. 50 min prior.

I don't lose face... anyone who worries about face is too uptight
to
solve real problems.

...Jim Thompson

hear, hear. Alas plenty of people like that. Me, I try to acknowledge
mistakes, and then try to learn from them. Having done a fair bit of
production engineering, I learned pretty early on that people
randomly
screw
stuff up, and its up to me as a designer to take that into account -
prevent
screw ups where possible (eg different plugs so you cant get it
wrong),
then
make sure screw-ups are blindingly obvious so they get caught early
on,
etc.
Besides, mistakes can be quite exciting with power electronics
(little
dutch
time bomb, tick-tock-boom).

Cheers
Terry


I've made so many mistakes in my lifetime that I doubt that any of you
will ever catch up ;-)

...Jim Thompson

I'm not going to let that stop me trying :} I work hard at not making
the
same mistake twice. Luckily there are plenty of other mistakes for me to
choose from, so I havent run out yet.

I must admit that I have, at least once, realized that I had made the same
mistake before. I work hard at not making the same mistake twice again,
so
that I will not have to make that admission again.
Click to expand...
I've done it a few times. Unfortunately none of the excuses I could come up
with were very flattering. hence the working hard not to do it again :}

Cheers
Terry
 
"Richard Henry" <rphenry@home.com> wrote in message
news:sR5tc.35660$PU5.35636@fed1read06...
"Dave VanHorn" <dvanhorn@cedar.net> wrote in message
news:GNWdnV_OI_SzNindRVn-jw@comcast.com...

Mobius strip?

To which posting was this a reply?
Click to expand...
I was wondering if anyone wanted to tackle that one.
 
"Dave VanHorn" <dvanhorn@cedar.net> wrote in message
news:7cGdnWt3xLrYqijdRVn-ug@comcast.com...
"Richard Henry" <rphenry@home.com> wrote in message
news:sR5tc.35660$PU5.35636@fed1read06...

"Dave VanHorn" <dvanhorn@cedar.net> wrote in message
news:GNWdnV_OI_SzNindRVn-jw@comcast.com...

Mobius strip?

To which posting was this a reply?

I was wondering if anyone wanted to tackle that one.

Where would you look for the resistance? Half-way between the edge?
Click to expand...

:)
Rich
 
"Terry Given" <the_domes@xtra.co.nz> wrote in message news:%H1tc.10441
"Jim Thompson" <thegreatone@example.com> wrote in message
On Wed, 26 May 2004 19:07:15 -0700, "Terry Given"
"Jim Thompson" <thegreatone@example.com> wrote in message
On Tue, 25 May 2004 21:50:08 -0400, Activ8 <reply2group@ndbbm.net
has lost "face" in a public forum. :( Perhaps a consolation prize
is
in order. Might I suggest a fine Klein bottle decanter for the
merlot
(would lead to better concentration and more wine in the food).
....
Besides, mistakes can be quite exciting with power electronics (little
dutch
time bomb, tick-tock-boom).
Terry
I've made so many mistakes in my lifetime that I doubt that any of you
will ever catch up ;-)
...Jim Thompson
I'm not going to let that stop me trying :} I work hard at not making the
same mistake twice. Luckily there are plenty of other mistakes for me to
choose from, so I havent run out yet.
Terry

Actually, a mistake is only a mistake in hindsight - at the time you
Click to expand...
did it, it seemed to be the right thing to do, or you wouldn't have
done it. So technically, nobody has ever made a mistake! :)

Cheers!
Rich
 
Jim Thompson <thegreatone@example.com> writes:

I've made so many mistakes in my lifetime that I doubt that any of you
will ever catch up ;-)
Click to expand...
As my ex-boss used to say:

"I never make mistakes... Well actually I did make one once, when one
time I thought I had made a mistake but I hadn't!"


--

John Devereux
 
Robert Baer wrote:
Activ8 wrote:

On 24 May 2004 19:12:09 -0500, The Phantom wrote:

On Mon, 24 May 2004 15:22:14 -0700, Chris Carlen
crcarle@BOGUS.sandia.gov> wrote:

Frank Bemelman wrote:
"Chris Carlen" <crcarle@BOGUS.sandia.gov> schreef in bericht
news:c8ta9v0183o@news4.newsguy.com...

Fun problem. Wasn't what I had originally planned for my first hour of
the day.

Your next assignment is the dodecahedron ;)


If you can draw it, I'll solve it.

Consider the infinite plane grid of 1 ohm resistors with nodes on
the coordinates with integer values, such as (1,1), (2,2), (1,2) etc.
None of the resistors is diagonally connected, as between (1,1) and
(2,2). All the horizontally adjacent and vertically adjacent nodes
have a 1 ohm resistor connected.

What is the resistance between the points (1,1) and (1,2)?

What is the resistance between the points (1,1) and (1,2)?

1,1 1,2 1,3
___ ___
+-|___|--+-|___|-+
| | |
.-. .-. .-.
| | A | | B | |
| | | | | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+
| | |
.-. .-. .-.
| | | | | |
| | C | | D | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ 3,3

Taking only mesh A, we get 1 ohm

Connecting mesh D, it's 2 ohms

scap that approach...

ok connect two equal potential points in both meshes A and D (1,2 to
2,1 and 2,3 to 3,2) and you get

2
1,2 ___ 2,3
+-------|___|--------+
| |
| |
.5 | .5 .5 | .5
___ | ___ ___ | ___
1,1 -|___|---+---|___|-----|___|--+--|___|- 3,3
| |
| |
| |
| |
| ___ |
+--------|___|-------+
2

that's 1.5 ohm or 3(.5)

and since a single 4 R mesh (like A only) would be 1 ohm,
(2,2)-(1,1) = 1,1 and (3,3)-(1,1)=2,2 so j=k is 1 or 2 i.e., the
dimension, n

n R
_____
1 1
2 1.5 crap! need one more

nah. skip the subtraction and go with n=j=k

n R
_____
2 1
3 1.5

R = .5n -- a wild first guess which would make the next higher
dimension grid

R = 2

1,1 1,2 1,3
___ ___
+-|___|--+-|___|-+ R +
| | |
.-. .-. .-.
| | A/ | | B | | R
| | | | | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ R +
| | |
.-. .-. .-.
| | | | / | | R
| | C | | D | |
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ R +
| | |
.-. .-. .-.
| | | | | | /
| | C | | D | | R
'-' '-' '-'
| ___ | ___ |
+-|___|--+-|___|-+ R + 4,4

er, it's a bit late for me to stare aat this any more to connect 1,4
with 4,1. I'd rather do a mesh or node analysis at this point.
--
Best Regards,
Mike

Hmm.. not necessarily leading to an answer, but thinking slow and
"out loud"..

1,1 1,2 1,3
___ ___
+-|_a_|--+-|_b_|-+
| | |
.-. .-. .-.
| | A | | B | |
|c| |d| |e|
'-' '-' '-'
| ___ | ___ |
+-|_f_|--+-|_g_|-+
| | |
.-. .-. .-.
| | | | | |
|h| C |j| D |k|
'-' '-' '-'
| ___ | ___ |
+-|_m_|--+-|_n_|-+ 3,3

Taking the idea of adding resistors b+e=p and h+m=q..

1,1 1,2
___ ___
+-|_a_|--+-|_p_|-+
| | |
.-. .-. |
| | A | | |
|c| |d| |
'-' '-' |
| ___ | ___ |
+-|_f_|--+-|_g_|-+
| | |
| .-. .-.
| | | | |
| |j| D |k|
| '-' '-'
| ___ | ___ |
+-|_q_|--+-|_n_|-+ 3,3

Then delta to wye..

1,1 1,2
___ ___
+-|_a_|--+-|_D_|-+
| |
.-. + ------+
| | A .-. .-.
|c| |P| |G|
'-' '-' '-'
| | |
.-. | |
|J| +----+ |
'-' .-. .-. .-.
| |Q| | | | |
| '-' |j| D |k|
+---+ '-' '-'
| ___ | ___ |
+-|_F_|--+-|_n_|-+ 3,3

Well, it is partly simplified; i used capital letters for the
"diagonal" or "corner" or "compliment" resistors (do not know the proper
term); value seems to be 1/3 ohm each.

Someone else can take it from here...
Click to expand...
I blew it on the drawing and delta to wye conversion.
As soon as i got off the web, i "saw" it..as simple as the cube
problem.
One shorts across the diagonal.
So for the 2 by 2, the current splits first by 2 then by 4, back to
two for 1.5 ohm corner to corner resistance.
Then for a 4 by 4, the current splits by 2, by 4, by 6, then by 8;
corner to corner resistance is 25/12 ohms.
An 8 by 8 array gives 2283/840 ohms.
Seems that useage of a Fibonacci series would be useful for
generalization purposes.
 
Rich Grise <null@example.net> says...

Actually, a mistake is only a mistake in hindsight - at the time you
did it, it seemed to be the right thing to do, or you wouldn't have
done it. So technically, nobody has ever made a mistake! :)
Click to expand...
I remember thinking as I opened that third bottle of wine,
"this is a mistake"...
 
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