Simple Question

It won't fit on a finite page.

-- _____ _ _ |_ _| | | | | | | __ _ _ __ ___ | |__| | ___ _ __ ___ ___ _ __ | | / _` | '_ ` _ \\ | __ |/ _ \\| '_ ` _ \\ / _ \\ '__| _| |_ | (_| | | | | | | | | | | (_) | | | | | | __/ | |_____| \\__,_|_| |_| |_| |_| |_|\\___/|_| |_| |_|\\___|_| __ ____ / _| | _ \\ ___ | |_ | |_) | ___ _ __ __ _ / _ \\| _| | _ < / _ \\| '__/ _` | | (_) | | | |_) | (_) | | | (_| |_ \\___/|_| |____/ \\___/|_| \\__, (_) __/ | |___/

Carefully, I'd say.

-- _____ _ _ |_ _| | | | | | | __ _ _ __ ___ | |__| | ___ _ __ ___ ___ _ __ | | / _` | '_ ` _ \\ | __ |/ _ \\| '_ ` _ \\ / _ \\ '__| _| |_ | (_| | | | | | | | | | | (_) | | | | | | __/ | |_____| \\__,_|_| |_| |_| |_| |_|\\___/|_| |_| |_|\\___|_| __ ____ / _| | _ \\ ___ | |_ | |_) | ___ _ __ __ _ / _ \\| _| | _ < / _ \\| '__/ _` | | (_) | | | |_) | (_) | | | (_| |_ \\___/|_| |____/ \\___/|_| \\__, (_) __/ | |___/

-- . . . . . . . .

Hehe. Then use infinitely small type and you can get it into a finite space. (Infinite sum of infinitely small values can be made finite.)

;)

Jon

Here's a site that covers the details better than I probably can find time to achieve:

and

It looks as though I was on safe territory.

Jon

it's simple, they are looking for chess players., i don't play chess!

Sorry. That last link should be:

It was linked to by the bottom of the first link I gave before, which was correct.

Jon

My answer would have been zero ohms.

Zero looks good to me, using the reciprical of a series of even half fractions that would seem to approach zero. But thats a wild ass guess based on stale math skills.

Not necessarily. Observing how a candidate handles such problems can be interesting, irrespective of whether their answer is, in the end, correct.

"jntel" schrieb im Newsbeitrag news:K_zRg.4740$ snipped-for-privacy@newssvr25.news.prodigy.net...

I believe that you are correct. The theory: If you connect two resistors in parallel, the resulting resistance is always lower than the lowest of either's values. So, if you connect an infinite number of resistors in parallel, the value is infinitely lower, which is, by definition, 0. The practice: An infinite number of connected resistors, measured across two arbitrary points, behaves just like an infintely large capacitor (due to the tiny capacitances of the resistors adding up). An infinitely large capacitor takes an infinite time to charge, and during this time, exhibits a resistance of 0 Ohms, which is what you would measure with an ohm meter. In other words, the current simply gets lost ;-) Nothing is more practical than a good theory - QED ;-)

Leo

But this wasn't the case here, at least as I understood the problem. The original post described an infinite "grid" of resistors - i.e., imagine an infinitely large grid of squares, with each "node" (every point within the grid where the corners of the squares meet) connected to the adjacent nodes by a one-ohm resistor. Now measure the resistance between any two adjacent nodes, and see what you get.

The answer clearly can't be zero. The situation is actually very analogous to determining the resistance between two points separated by a finite distance, but within an infinite plane of some conductive (but not perfectly conductive) material. For instance, imagine a very large sheet of thin copper; put the probes of your ohmmeter (which presumably has a scale for sufficiently low resistances) an inch apart in the middle of the sheet - what should you read?

Bob M.

Yes. It's less than 3 ohms but more than zero.

The fun is in deducing theory to specifics and solving quantitatively. Otherwise, there is no way to see if theory holds. I think I got the details right, using two completely different approaches to the problem and providing similar results.

Jon

Sorry, forgot to add:

Now we need to find someone with that infinite matrix, or one sufficiently so, so we can test the approaches.

A 100x100 grid should be good enough: 99*100*2 or 19800 1-ohm resistors. Digikey has axials down to 2.2 ohms, so make it 10 ohms for ease of relating values. Hmm, $1260.00 for 5000 of them. So that makes it about $4,990.00. Cheap. Only $5k to test this idea out, plus a little solder and work.

Volunteers and donations?

In the interests of science?

Jon

We have mathematics. We don't need solder.

Oh, no! Science is _theory_ _and_ _result_. Not just _theory_. Not just _result_. But both. We need to _test_ the theory. See what nature shows us. Might find something new in the process, too. Perhaps a new effect, hitherto unaccounted for. Could be important, you know. :)

We just need that money and volunteer time. I did the hard stuff, so I'm off the hook. ;)

Jon

Well, you also must consider that at some point in the grid - the measuring voltage and current would become to low to even conduct thru a 1 ohm resistor. So it would not divide infinitely. So why build a grid so large to test the theory. Assemble a grid of say 10 x 10 of the 4 resistor cube. 121 resistors are more manageable and I think that would get close the the answer. JTT

"James Thompson" wrote in news:da4c1$451a04dd$438c84a1$ snipped-for-privacy@ALLTEL.NET:

Probability and Statistics. The larger your sample size, the smaller the effect of any one given outlier.

Btw, I think we could probably make one ohm resistors. Simply take a length of 24 ga wire and wrap it back and forth (to eat up length) until its value = 1 ohm. Repeat until you've got enough resistors to test the theory. Why do we need those 10 ohm things?

Puckdropper

See? More's the reason for those 10 ohm. Or even 100 ohm.

But in my last sentence you quoted I was teasing, in case it wasn't clear. (Mostly about some of the differences between the lives of theorists and experimentalists.)

Jon

P.S. By the way, I'm pretty sure the figure is as I stated it was.