[math-fun] The Uncracked Problem with 33
33 is the lowest unsolved problem in "summing three cubes" with Tim Browning. https://www.youtube.com/watch?v=wymmCdLdPvM
Dear math-fans, Here is a video of the Offset Somsky Gears: https://www.youtube.com/watch?v=ekZGCVFajqc People are asking me about the mathematics of Somsky Gears and the Offset Somsky Gears. Unfortunately, the math-fun discussions are private and unstructured. Is there any public explanation available? So far, I know only Tom Rokicki's Somsky Solver at http://tomas.rokicki.com/somsky.html. This is great for providing insight, but it does not explain how or why it works. Thank you. Oskar
On 11/8/15, M. Oskar van Deventer <m.o.vandeventer@planet.nl> wrote:
Dear math-fans,
Here is a video of the Offset Somsky Gears: https://www.youtube.com/watch?v=ekZGCVFajqc
People are asking me about the mathematics of Somsky Gears and the Offset Somsky Gears. Unfortunately, the math-fun discussions are private and unstructured. Is there any public explanation available? So far, I know only
Tom Rokicki's Somsky Solver at http://tomas.rokicki.com/somsky.html. This is
great for providing insight, but it does not explain how or why it works.
Thank you.
Oskar
Note that the ring radius also increases when the planets increase, which I don't think was mentioned in the commentary. I'm still trying to put a coherent account of the mathematics together, but it keeps running away in different directions ... maybe WRS has had better luck? Along with the video are listed a number of other ingenious gear models, including "Flower Gears" at https://www.youtube.com/watch?v=AFsKvanfYbQ --- an epically disastrous attempt to construct an elaborate multi-level planetary gear system which disintegrates in a shower of cogs when any attempt is made to demonstrate its intended function. It drew my attention because of the analogy with my recent abortive "octocog" project, and I am fairly sure that it fails for essentially the same reason. Inspection reveals 3 distinct hexagonal circuits of gears, each of which must admit an endless belt of exactly integer length. In addition, the outer ring must have radius exactly an integer (given the radii of the planets, here all equal to 5). The total number of continuous constraints is 4, so there is almost certainly no nontrivial exact solution. By tinkering with the planet radii and floral pattern --- all discrete variables --- it will be possible to find approximate solutions, of which I am fairly sure "Flower Gears" is an example: and the larger the radii involved, the better the potential approximation. But I assume that Oskar found his via experimentation, without actually calculating either exact belt lengths or ring radius. The fudge duly came home to roost; although even if exact, such a mechanism would probably require subframes supporting intermediate levels. Fred Lunnon
Nice video, thanks for the link. I just checked the OEIS, where the relevant sequence is https://oeis.org/A060464, and I was happy to see that Charles Greathouse already added a link there to the video Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sat, Nov 7, 2015 at 10:37 PM, Stuart Anderson < stuart.errol.anderson@gmail.com> wrote:
33 is the lowest unsolved problem in "summing three cubes" with Tim Browning. https://www.youtube.com/watch?v=wymmCdLdPvM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Here's an imprecisely-stated question about the OEIS that I've had for awhile. What are its "most misplaced" entries? For example the Fibonacci sequence at A000045 is hardly misplaced. Is there something past 50,000 that "should" be in the top 200? (I have no definition for "should" in mind...I welcome potential ideas.) Conversely, is there something in the top 100 that no one is ever looking for? On Mon, Nov 9, 2015 at 9:56 AM, Neil Sloane <njasloane@gmail.com> wrote:
Nice video, thanks for the link. I just checked the OEIS, where the relevant sequence is https://oeis.org/A060464, and I was happy to see that Charles Greathouse already added a link there to the video
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Nov 7, 2015 at 10:37 PM, Stuart Anderson < stuart.errol.anderson@gmail.com> wrote:
33 is the lowest unsolved problem in "summing three cubes" with Tim Browning. https://www.youtube.com/watch?v=wymmCdLdPvM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
A3 (aka A000003) is a bit of a wallflower, probably isn't often looked up In the other direction, you could look at the sequences with keyword "core". There is an entry in the Index to the OEIS for them Here are the last 3 lines of the Index entry (see https://oeis.org/wiki/Index_to_OEIS:_Section_Cor): core sequences, (09): A004526 <http://oeis.org/A004526> (ints repeated), A005036 <http://oeis.org/A005036> (dissections), A005100 <http://oeis.org/A005100> (deficient), A005101 <http://oeis.org/A005101> (abundant), A005117 <http://oeis.org/A005117>(squarefree), A005130 <http://oeis.org/A005130> (Robbins), A005230 <http://oeis.org/A005230> (Stern), A005408 <http://oeis.org/A005408> (odd), A005470 <http://oeis.org/A005470> (planar graphs), A005588 <http://oeis.org/A005588> (binary rooted trees), A005811 <http://oeis.org/A005811> (runs in n), A005843 <http://oeis.org/A005843> (even), A006318 <http://oeis.org/A006318> (royal paths or Schroeder numbers), A006530 <http://oeis.org/A006530> (largest prime factor)core sequences, (10): A006882 <http://oeis.org/A006882> (n!!), A006894 <http://oeis.org/A006894> (3-trees), A006966 <http://oeis.org/A006966> (lattices), A007318 <http://oeis.org/A007318> (Pascal's triangle), A008275 <http://oeis.org/A008275> (Stirling 1), A008277 <http://oeis.org/A008277> (Stirling 2), A008279 <http://oeis.org/A008279> (permutations k at a time), A008292 <http://oeis.org/A008292> (Eulerian), A008683 <http://oeis.org/A008683> (Moebius), A010060 <http://oeis.org/A010060> (Thue-Morse), A018252 <http://oeis.org/A018252> (nonprimes), A020639 <http://oeis.org/A020639> (smallest prime factor), A020652 <http://oeis.org/A020652> (fractal), A020653 <http://oeis.org/A020653> (fractal), A027641 <http://oeis.org/A027641> (Bernoulli),A027642 <http://oeis.org/A027642> (Bernoulli), A035099 <http://oeis.org/A035099> (j_2), A038566 <http://oeis.org/A038566> (fractal), A038567 <http://oeis.org/A038567> (fractal), A038568 <http://oeis.org/A038568> (fractal), A038569 <http://oeis.org/A038569> (fractal), A049310 <http://oeis.org/A049310>(Chebyshev), A253240 <http://oeis.org/A253240> (cyclotomic polynomial)core sequences, (11): A070939 <http://oeis.org/A070939> (binary length), A074206 <http://oeis.org/A074206> (ordered factorizations), A104725 <http://oeis.org/A104725> (complementing systems) Most of them could have had lower A-numbers. By the way, A22 (Cayley, 1874) never received much attention until sequence A053873 (n is in A_n) and A053169 (n is not in A_n) came up. Eric Rains and I wrote a paper about it (see A000022 for the link), whose unofficial purpose was to compute enough terms of A22 to answer the question (Cayley hadn't given enough terms and the definition was somewhat obscure) Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Mon, Nov 9, 2015 at 1:28 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
Here's an imprecisely-stated question about the OEIS that I've had for awhile. What are its "most misplaced" entries? For example the Fibonacci sequence at A000045 is hardly misplaced.
Is there something past 50,000 that "should" be in the top 200? (I have no definition for "should" in mind...I welcome potential ideas.) Conversely, is there something in the top 100 that no one is ever looking for?
On Mon, Nov 9, 2015 at 9:56 AM, Neil Sloane <njasloane@gmail.com> wrote:
Nice video, thanks for the link. I just checked the OEIS, where the relevant sequence is https://oeis.org/A060464, and I was happy to see that Charles Greathouse already added a link there to the video
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Nov 7, 2015 at 10:37 PM, Stuart Anderson < stuart.errol.anderson@gmail.com> wrote:
33 is the lowest unsolved problem in "summing three cubes" with Tim Browning. https://www.youtube.com/watch?v=wymmCdLdPvM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
A few possibilities include: A052432 Smallest conductor of elliptic curve with rank n. A053624 Highly composite odd numbers. A053644 Most significant bit of n. A053695 Differences between record prime gaps. A054504 Numbers n such that Mordell's equation y^2 = x^3 + n has no integral solutions. but I don't know of a good way to find such sequences except by looking. As for unpopular sequences, A000017 is a good candidate, being marked "dead" as an erroneous duplicate of a (later) sequence. A000038 is easy and pretty niche. A000053 and A000054 are often mentioned in discussions of what a sequence could be but I don't think anyone looks them up. Charles Greathouse Analyst/Programmer Case Western Reserve University On Mon, Nov 9, 2015 at 1:28 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
Here's an imprecisely-stated question about the OEIS that I've had for awhile. What are its "most misplaced" entries? For example the Fibonacci sequence at A000045 is hardly misplaced.
Is there something past 50,000 that "should" be in the top 200? (I have no definition for "should" in mind...I welcome potential ideas.) Conversely, is there something in the top 100 that no one is ever looking for?
On Mon, Nov 9, 2015 at 9:56 AM, Neil Sloane <njasloane@gmail.com> wrote:
Nice video, thanks for the link. I just checked the OEIS, where the relevant sequence is https://oeis.org/A060464, and I was happy to see that Charles Greathouse already added a link there to the video
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Nov 7, 2015 at 10:37 PM, Stuart Anderson < stuart.errol.anderson@gmail.com> wrote:
33 is the lowest unsolved problem in "summing three cubes" with Tim Browning. https://www.youtube.com/watch?v=wymmCdLdPvM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
And yet -- a dictionary must still have entries for "the", "of", "take", and "and", even though these entries are rarely referred to. On Tue, Nov 10, 2015 at 11:27 AM, Charles Greathouse < charles.greathouse@case.edu> wrote:
A few possibilities include: A052432 Smallest conductor of elliptic curve with rank n. A053624 Highly composite odd numbers. A053644 Most significant bit of n. A053695 Differences between record prime gaps. A054504 Numbers n such that Mordell's equation y^2 = x^3 + n has no integral solutions. but I don't know of a good way to find such sequences except by looking.
As for unpopular sequences, A000017 is a good candidate, being marked "dead" as an erroneous duplicate of a (later) sequence. A000038 is easy and pretty niche. A000053 and A000054 are often mentioned in discussions of what a sequence could be but I don't think anyone looks them up.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Mon, Nov 9, 2015 at 1:28 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
Here's an imprecisely-stated question about the OEIS that I've had for awhile. What are its "most misplaced" entries? For example the Fibonacci sequence at A000045 is hardly misplaced.
Is there something past 50,000 that "should" be in the top 200? (I have no definition for "should" in mind...I welcome potential ideas.) Conversely, is there something in the top 100 that no one is ever looking for?
On Mon, Nov 9, 2015 at 9:56 AM, Neil Sloane <njasloane@gmail.com> wrote:
Nice video, thanks for the link. I just checked the OEIS, where the relevant sequence is https://oeis.org/A060464, and I was happy to see that Charles Greathouse already added a link there to the video
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Nov 7, 2015 at 10:37 PM, Stuart Anderson < stuart.errol.anderson@gmail.com> wrote:
33 is the lowest unsolved problem in "summing three cubes" with Tim Browning. https://www.youtube.com/watch?v=wymmCdLdPvM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (7)
-
Allan Wechsler -
Charles Greathouse -
Fred Lunnon -
M. Oskar van Deventer -
Neil Sloane -
Stuart Anderson -
Thane Plambeck