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posted by
janrinok
on Sunday March 02 2014, @08:30PM
from the keeping-geeks-and-mathematicians-happy dept.
from the keeping-geeks-and-mathematicians-happy dept.
KritonK writes:
Ed's Note: For those not sure what an optimal Golomb ruler is, or how you would use one, see here.
"Following the recent start of the OGR-28 project, the search for the optimal Golomb ruler with 28 marks, distributed.net quietly announced the completion of project OGR-27 on February 25. The shortest Golomb ruler with 27 marks has length 553 and marks at positions 0 3 15 41 66 95 97 106 142 152 220 221 225 242 295 330 338 354 382 388 402 415 486 504 523 546 553. This confirms that the best known, up to now, Golomb ruler was optimal. When the project began, it was expected that a shorter ruler would be found, but this did not happen."
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The OGR-27 Project Has Been Completed
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(Score: 5, Funny) by Appalbarry on Sunday March 02 2014, @08:43PM
Man, I can't recall how many times I was reading Slashdot, and thought to myself, "Where are the updates on Golomb ruler research?"
Actually, I've been pretty amazed at the quality of what gets posted to SN - smart, interesting stuff, a lot of which I would never have seen.
Now, imagine a Beowolf cluster of Golomb rulers!
(Score: 3, Interesting) by VLM on Sunday March 02 2014, @09:28PM
"Now, imagine a Beowolf cluster of Golomb rulers!"
That would just be a big pile of varying length rulers ... two of which (reversed) are shortest, aside from some really small ones where there are even number of duplicates all the same short length. Boring.
I would be amazed if a zillion years from now someone discovered OGR-75 is a triple or something like that. Want to impress the local extraterrestrials with your math abilities? Send them a really long list of OGRs. I don't remember any proofs about OGR duplicates. Maybe no long ones exist only short.
A cluster of Optimal GR would vaguely resemble a radio telescope array or whatever else they're being used for now.
I always thought a funny ardweeeeeeeeeeenio project would be a real world OGR-15 with LEDs on the correct centimeter spaces (it'll be about 5 feet long?) and a display and dial and you dial up "hey OGR-15 gimmie 9 cm" and it'll figure out which two LEDs to illuminate to provide you with 9 cm, assuming it exists (no perfect rulers exist beyond some short length, I think?). In my infinite spare time of course. That would obviously be an incredibly handy ruler for the machine shop, which I'm sure I would use daily.
(Score: 1) by egcagrac0 on Sunday March 02 2014, @10:29PM
Most LEDs I see aren't small enough to be useful as ruler ticks.
Laser emitters have potential, but aligning them all to parallel would be a pain.
Two lasers with two mirrors on two leadscrews, on the other hand, would allow you to dial in two arbitrary positions, limited by backlash and screw calibration (but those are already commonly addressed in a machine shop).
(Score: 2) by VLM on Sunday March 02 2014, @10:36PM
Yeah but that wouldn't be an OGR application. I was aiming at more of an educational "science fair demonstration" kind of thing. Ahhh I see how it works by turning the dial to select different lengths type of thing.
(Score: 1) by egcagrac0 on Monday March 03 2014, @12:25AM
Absolutely true. It's a valid visualization tool, but not a practical application.
A practical application of such a system would be for, say, current transformers, or a resistance substitution box.
(Score: 0) by neagix on Sunday March 02 2014, @10:11PM
before the Beowulf cluster mention, I was buying it that you were serious..