December 2012 - mathfun@mailman.xmission.com

[math-fun] Meta: math-fun password?
by Mike Stay 19 Dec '12

19 Dec '12

I wanted to hunt through the archive a few minutes ago, but realized I've forgotten whatever password I used when I subscribed many years ago. The page says it should be mailed to me in cleartext periodically, but I don't recall ever having received such an email and searching my archive turns up nothing. I don't see a way to trigger a password reminder, either. Help? -- Mike Stay - metaweta(a)gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com

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[math-fun] Greedily packing disks in a sector
by James Propp 19 Dec '12

19 Dec '12

What do you get if you start packing unit disks in a 72-degree sector of the plane, placing each successive disk as close as possible to the corner? Some sort of quasiperiodic structure? Jim Propp

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Re: [math-fun] Exhibit for MoMath?
by Bill Gosper 18 Dec '12

18 Dec '12

(Sorry about RoundCube(?) losing the indentation below.) GH>Bob, That would have been the Mathematica exhibit, by Charles and Ray Eames. I remember seeing it as a kid at the NY World's Fair, and I'm sure it had a positive effect on my interest in math. There's a restored copy on display now at the NY Hall of Science in Queens. http://en.wikipedia.org/wiki/Mathematica:_A_World_of_Numbers..._and_Beyond I agree it is fine to replicate exhibits from elsewhere, but I wanted to create novel ones for MoMath while I had the opportunity and budget. If MoMath creates enough interest, there will be math museums in cities all across the country and the best math exhibits should be replicated widely. George http://georgehart.com/ On 12/17/2012 11:07 AM, Robert Baillie wrote: what's wrong with wonderful exhibits that do happen to be elsewhere? the kids who visit moma probably won't see exhibits that are in, say, chicago. i remember two great exhibits from the museum of science and industry in chicago from the 1960's: a) drop a bunch of pingpong balls through a lattice of obstructions into bins at the bottom and watch the bell curve form; b) soap films! bob baillie --- George Hart wrote: Bill, That's a fairly common exhibit that I've seen at many science museums. As you point out, one of its limitations is that it only demonstrates the theorem for a single triangle. For MoMath, I wanted to create all new exhibits, not found anywhere else. So I came up with a variation in which the triangle was adjustable. The C^2 is always the same, but the right angle moves along a semicircle, so the legs can vary and sliding components change the leg squares appropriately. We engineered a way where it was feasible, not with a fluid (which would leak), but with a fixed volume of small beads. In the end it didn't make the final cut of exhibits. However, it's possible it may show up as a replacement exhibit at some time in the future. George http://georgehart.com/ On 12/17/2012 1:03 AM, Bill Gosper wrote: Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg (Gaa, now it won't UNindent!) Well, an advantage of several similar mechanisms side by side is that multiple kids can experiment. Pursuing this, repeat the several triangles with their surrounding squares replaced by semicircles and again by regular pentagons, say. A theorem this important deserves multiple coverage. And to balance squishy with crunchy, some mechanization of http://gosper.org/perigal.htm . Which raises the possibility of other dissections when the three bounding figures are other than squares. --rwg

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[math-fun] Crowdfunding math research
by Henry Baker 18 Dec '12

18 Dec '12

Getting funding for pure math research can be difficult, but perhaps there is now a new way. Some of you have heard about "crowdsourcing" & possibly "crowdfunding" -- e.g., Kickstarter.com. Below is a link to a recent 90-minute video from UCSB about getting funding for projects through crowdfunding. I would imagine that if someone were doing cool fractal structures, including perhaps cool 3D-printed fractals, such funding might be easy. If someone were working on the (incredibly cool) Bailey/Borwein/Plouffe-type spigots, it might catch the excitement of a large number of people. If someone were building Antikthera mechanisms for the mantelpiece, there might be a market. If someone built a Solar System pinball machine (in software -- perhaps eventually for the XBox), there might be some takers. If someone built a Eureqa-type program, but more oriented towards number theory, there might be some takers. --- "Crowdfunding for Academic Research" 10/19/2012 http://www.youtube.com/watch?v=BvdRuiqIUI8

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[math-fun] Exhibit for MoMath?
by Bill Gosper 17 Dec '12

17 Dec '12

Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg

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[math-fun] National Math Museum Opens in NYC
by Henry Baker 17 Dec '12

17 Dec '12

FYI -- http://www.nytimes.com/aponline/2012/12/17/nyregion/ap-us-travel-brief-nyc-… National Math Museum Opens in NYC By THE ASSOCIATED PRESS Published: December 17, 2012 at 8:44 AM ET NEW YORK (AP) Â There is wonder in numbers, and the curators of a new museum in New York City hope to prove it. The National Museum of Mathematics opened to the public Saturday in Manhattan. The museum is aimed at kids aged 8 to 13, and curators have given the place a playground feel. The 40 exhibits include a "wall of fire" made up of laser lights that teaches kids about geometry and a square-wheeled tricycle that still manages to produce a smooth ride thanks to a wavy track. Founder Glen Whitney says the idea is to show people the "fun, beautiful" things done with mathematics. The museum occupies the first two floors of an office tower across from Madison Square Park at 11 E. 26th St. Tickets are $15 for adults and $9 for children. The museum is open daily 10 a.m. to 5 p.m. ___ Online: http://momath.org/

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[math-fun] A New Glimpse into the Mind of Ramanujan
by Hans Havermann 17 Dec '12

17 Dec '12

Carol Clark writes about Emory University mathematician Ken Ono and his students' insight: "For the first time, we can prove that the exotic functions that Ramanujan conjured in his death-bed letter behave exactly as he said they would, in every case." http://esciencecommons.blogspot.ca/2012/12/math-formula-gives-new-glimpse-i…

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[math-fun] Ain't no more matter particles, found them all?
by Warren Smith 16 Dec '12

16 Dec '12

Otto Eberhardt & 6 others: Impact of a Higgs Boson at a Mass of 126 GeV on the Standard Model with Three and Four Fermion Generations, Phys. Rev. Lett. 109,24 (2012) 241802 http://arxiv.org/abs/1209.1101 Press release: http://www.kit.edu/visit/pi_2012_12398.php QUOTE “But why does nature have second and third generations, if these are hardly needed? And are there maybe more generations of particles?”, ask the main authors of the article, Martin Wiebusch and Otto Eberhardt. At least, the latter question is answered: “There are exactly three fermion generations in the standard model of particle physics!” For their analysis, the researchers combined latest data collected by the particle accelerators LHC and Tevatron with many known measurements results relating to particles, such as the Z-boson or the top-quark. The result of the statistical analysis is that the existence of further fermions can be excluded with a probability of 99.99999 percent (5.3 sigma). The most important data used for this analysis come from the recently discovered Higgs particle. END QUOTE You may wonder how the hell they can rule out the existence of further particles. For example, if there were some 4th kind of lepton (the 3 known kinds are electron, muon, and tauon, the latter two being unstable) or quark, or neutrino, with huge mass-energy, then due to the postulated hugeness presumably it would have no effect on anything we are capable of observing, so it might well exist for all our experiments can tell... right? I think their reasoning is something like the following. They presume that a large fraction of the "mass" of the new particles is not mass per se, but rather is effective mass due to interaction-energy with the all-pervading Higgs scalar field. It is this "Higgs mechanism" that allows the W and Z vector bosons to have effective mass even though in Yang-Mills theory they necessarily have zero mass, thus rescuing and enabling Yang-Mills theory to be physically real. Their point: given this is the cause of the new particles having most of their mass, the Higgs is going to have something to say about that. If it were assumed to have enormous interactions, then the Higgs ought to have enough-altered physics we would have seen that, which we do not. So I think their idea is: if the new particles had small masses we would have seen them. If they had large masses due to Higgs effect, we would have seen Higgs bosons alterations that we do not. Therefore, there are no more kinds of new particles, QED. I do not know whether I believe this, and may be incompetent to decide. But it is an interesting line of reasoning. And the effects of this line of reasoning could be devastating to numerous theories of particle physics. But I see an obvious huge problem. We know that new particles must exist because of "dark matter" which has been detected gravitationally and outweighs the normal matter in the universe. If this mainstream view is correct, then this new paper yields an immediate proof that 1=0. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Binary Circulant Determinant equals Number
by Hans Havermann 15 Dec '12

15 Dec '12

Giovanni Resta has just come up with this size-36 circulant matrix, the determinant of which (34505916416) is equal to the the top line: 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 This is the largest (and only the seventh nontrivial) example of the genre.

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[math-fun] MoMATH
by Warren Smith 14 Dec '12

14 Dec '12

Museum of Maths opening in NYC http://momath.org/ 11 East 26th Street in Manhattan video: http://www.youtube.com/watch?v=jK7xPo1YXzY The video gives the impression this math museum is really more of a giant work of art than math per se. Two errors: 0:43 "a minimum spanning tree, the shortest possible way to ensure everyone is connected." Actually, the Steiner Minimum Tree is the shortest, and is in general shorter than the MST. Which incidentally is a highly interesting unfinished story. In any metric space, the SMT can be at most a constant factor shorter than the MST. The constant factor was exactly determined by F.Hwang & D.Z.Du in the plane; it is achieved for 3 sites forming equilateral triangle. However, many years later, it was pointed out that their proof is broken. Their result is probably true but remains conjectural. In 3-space yours truly made the conjecture the constant factor is achieved by a certain helical point set I call the "d-sausage" with d=3. This conjecture is also open. If d>=3 Du and I disproved the conjecture the constant arises from d+1 points in d-space forming a regular simplex, and our paper gave 3 disproofs. It was just recently pointed out that 2 out of our 3 disproofs are wrong. My disproof based on the d-sausage is the correct one; Du's disproofs were based on a "packing principle" which was refuted. It now might be conjectured if you are brave, that the d-sausage is optimal in d-space for every d>=3; Du had given an argument this should stop being true for large-enough d, but his argument is wrong since based on packing principle. 3:42 the Reuleaux triangle has constant WIDTH ("constant diameter" is a triviality, every shape has constant diameter). It can be used to drill an almost-square hole. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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