September 2006 - mathfun@mailman.xmission.com

[math-fun] Lost in fraction
by Eric Angelini 05 Sep '06

05 Sep '06

Hello, is there a (simple) fraction whose result is : 12.4635 4635 4635 4635 ... ? Best, É.

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[math-fun] Re: Melbourne, city of Math
by James Propp 05 Sep '06

05 Sep '06

George Hart writes: >Michigan artist David Barr designed his "Four Corners Project" in 1976. It is >an Earth-sized regular tetrahedron that spans the planet, with just the tips of >its four corners protruding. These visible portions are four-inch tetrahedra, >which protrude from the globe at Easter Island, Greenland, New Guinea, and the >Kalahari Desert. Barr traveled to these locations and was able to permanently >install the four aligned marble tetrahedra between 1981 and 1985. Glad to see someone's already done it! Though I should say I liked Dan Asimov's idea of using cylindrical tubes, which wasn't part of Barr's conception (and probably couldn't have been, given mid-70s technology). Michael Kleber writes: >I think the four "tetrahedron vertex" sculptures sounds like an >outstanding art project. If none of Jim's suggestions work, surely >there's someone who made far too much money in the dot-com >boom, who's just sitting around waiting to fund something like this! If there's some mathematically inclined dot-com zillionaire out there (a Google googolionaire, perhaps?) who's looking for something else fun to build, might I suggest a scaled-up, climbable version of the Boy's Surface sculpture at Oberwolfach? Jim

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Re: [math-fun] Earth polyhedra
by Daniel Asimov 04 Sep '06

04 Sep '06

Neil writes: << Many years ago i saw an abstract in the Oberwolfach Vortragsbuch entitled "Squares in Lake Michigan", which for a long time I thought proved theorems such as "any Jordan curve - or distorted circle in the plane - contains 4 points which are at the vertices of a square". But I never saw anything more about this, and began to doubt my memory. . . . >> When I was about 12, I recall reading the same statement in a popular math book -- it was either Mathematical Snapshots, by Hugo Steinhaus, or Through the Mathescope, by C. Stanley Ogilvy. If anyone has access to the right one of these, maybe it contains a reference. Then again, I seem to recall hearing years later (but also years ago) that this theorem had never been properly proved. --Dan

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Re: [math-fun] Earth polyhedra
by Fred W. Helenius 04 Sep '06

04 Sep '06

At 05:47 PM 9/4/2006, Schroeppel, Richard wrote: >On other subjects, specifically land-based tetrahedra: >Have we looked for land-based octahedra or cubes? In 1996, when I found the land-based tetrahedron that Jim Propp mentioned, I also looked for an octahedron. There seemed to be no hope for an island-free answer, and the only suitable island vertex I came up with was Palmyra Atoll. At the time I thought there might not be much land there at high tide, but apparently there is about a square mile of it. The location has since been acquired by the Nature Conservancy, which has information and pictures on their website: http://www.nature.org/wherewework/asiapacific/palmyra/ . (The antipodal point of Palmyra has also undergone some changes in the intervening decade; the country was then called Zaire, now it's the Democratic Republic of the Congo.) Here are the vertices of the octahedron: 5.87 N, 162.10 W Palmyra Atoll 5.87 S, 17.90 E D.R. Congo, near Kikwit 75.00 N, 49.55 W north central Greenland 75.00 S, 130.45 E Antarctica, Wilkes Land 13.76 S, 73.54 W Peru, west of Cuzco 13.76 N, 106.46 E northeastern Cambodia This assumes a spherical earth; unlike the tetrahedron, finding a geometrically precise octahedron on the real, non-spherical Earth will require points not quite on the surface. In particular, the points in Greenland and Antarctica are closer to each other than the other antipodal pairs. I found these polyhedra by examining an old-fashioned paper atlas, using a computer only to do the trigonometry. Finding a land cube this way seems unlikely. It's tricky enough to find any land tetrahedron; finding a cube amounts to finding a tetrahedron for which each the antipodal point of each vertex is also on land. It would be interesting see whether more and better results could be achieved using a contemporary GIS. -- Fred W. Helenius fredh(a)ix.netcom.com

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[math-fun] likely new Mersenne prime; Earth polyhedra
by Schroeppel, Richard 04 Sep '06

04 Sep '06

George Woltman reports (on the GIMPS mailing list) that a computer has reported finding a new Mersenne prime. If confirmed, this would be the 44th known. I assume GW is ringing up friends with fast machines (and independent software) to confirm the result. <rcs> Given the current ranges being tested, the size probably exceeds 10M digits, winning some kind of prize. A new quick-test was added to the GIMPS program a while back, which gives a pretty fast indication if the finding is real. (There have been one or two false reports caused by bugs or hardware problems.) The quick-test: The claiming computer forwards the Lucas residue from a few steps preceding the final 0. The receiver can do a few steps forward from this residue to validate the 0. The chance of a random residue passing this test is negligible, and we don't know of any way for a cheater to back up more than a couple of steps from a final (fake or real) 0, without taking more time than a Lucas test. ---- On other subjects, specifically land-based tetrahedra: Have we looked for land-based octahedra or cubes? I assume the Pacific Ocean would force any dodeca/icosa to have one or two vertex(ices) on an() island(s). Can we use the North Pole while it lasts? What about water-based polyhedra? This might need a database of lakes. Rich

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[math-fun] song of the week,
by Simon Plouffe 04 Sep '06

04 Sep '06

Hello (not serious), I received this song on a web site, 1 minute song with digits of pi. http://pi.ytmnd.com/ not so bad. simon plouffe

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Re: [math-fun] Re: Melbourne, city of Math
by Daniel Asimov 04 Sep '06

04 Sep '06

Jim writes: << I propose that someone build a tetrahedron with vertices at . . . (Thanks to Fred Helenius for identifying this "land tetrahedron". . .) . . . >> Hmmm, how about the connecting "beams" being (ends of) cylinders, upon each of which is a TV camera and inside of which is a TV screen showing what's at the other end? Plus, there may be nice arrangements of hundreds of such tetrahedra, so that everyone's "near" everyone. --Dan

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[math-fun] article on the Poincare' crowd
by Chris Landauer 03 Sep '06

03 Sep '06

hihi, all - there is also a short article on the same story in the economist for this week, but it is not nearly as good, and, surprisingly to me, it has several misleading phrases about the problem and its significance i also was impressed with the new yorker article, but mostly in how much they emphasized the conflicts instead of the cooperation (well, it seemed that way to me) i did nto study this area very much in school, but my favorite topology books were general topology (i think) by sze-tsen hu, and algebraci topology by spanier (the densest book i can remember successfulyl reading, ever) more later, cal

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Re: [math-fun] New Yorker article on the Poincare' crowd
by Daniel Asimov 03 Sep '06

03 Sep '06

Hilarie, aka The Purple Streak, writes: << The August 28 New Yorker has an article by Sylvia Nasar and David Gruber about the mathematicians who have contributed to the proof of the Poincare' conjecture: Hamilton the playboy, Yau of the infinite ambition, and Perelman the Pure (somehow Thurston escapes scrutiny, appearing merely as a mathematician with a brilliant conjecture). Yau comes off badly in this article. ... ... I don't think it explains the mathematical ideas particularly well ... >> I read the same article, and I found it well-written and fascinating; it's still available online, at < http://www.newyorker.com/fact/content/articles/060828fa_fact2 >. I'ts become quite a samizdat article among mathematicians; at least two people forwarded to me the article or link after I'd already read it (not counting Hilarie's mention of it). I thought the article did a pretty good job of explaining the mathematics, at least compared to any other article I've seen in a general publication, and especially a good job at describing the ambition and intrigue involved in claiming precedence on the "full" proof. Btw, I'm totally convinced the experts' consensus is that the Poincare conjecture is now fully settled in the affirmative; I'm not sure, however, whether the same is true of the Thurston geometrization conjecture. --Dan

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[math-fun] New Yorker article on the Poincare' crowd
by The Purple Streak, Hilarie Orman 02 Sep '06

02 Sep '06

The August 28 New Yorker has an article by Sylvia Nasar and David Gruber about the mathematicians who have contributed to the proof of the Poincare' conjecture: Hamilton the playboy, Yau of the infinite ambition, and Perelman the Pure (somehow Thurston escapes scrutiny, appearing merely as a mathematician with a brilliant conjecture). Yau comes off badly in this article. He and his students have undertaken the usually thankless task of fleshing out the proof sketches for major results like Perelman's. Yau added the twist of giving themselves the lion's share of the credit, relegating the original thought to an "important contribution". Both Yau and Perelman acknowledge Hamilton as having had the key idea, the Ricci flow. But in the subsequent 25 years he couldn't finish off the work. Too much windsurfing, perhaps? More importantly, a blindness to the young Russian. Perelman figuratively tugged at his coatsleeve, "Sir, I did some work that might apply." Hamilton was friendly but immersed in his own world. The contrast between Perelman and Yau makes for a great story. Perelman is younger and so unambitious that he has caused consternation. "Reclusive", "ascetic", "obsessed" are common descriptions. It's misleading. The reporters have an amusing story of trying to lure him out of his apartment for a meeting, acting a bit as though they were out to trap a squirrel. After three days, as a last resort, they knocked on the door and asked to see him. He was most gracious. I don't think the article will lead anyone to become a mathematician and I don't think it explains the mathematical ideas particularly well, but it's interesting to see mathematicians portrayed as personalities. Non-mathematical people will read this article and realize that there's drama to be had in even purest of academic pursuits. Hilarie

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