January 2013 - mathfun@mailman.xmission.com

Re: [math-fun] unclever wine rack
by Henry Baker 26 Jan '13

26 Jan '13

This email came through just fine. Does your email program believe in plain ascii? I've noticed that many messaging systems default to fancy formatted text, and sometimes have to be bludgeoned back into the ascii ages. Whenever I "cut & paste" text, I often have to check that it doesn't bring in formatting along with it. When pasting from a web page, I even resort to pasting it into Emacs/Xemacs first to kill the formatting, and then recutting & pasting into where it's really going to go. Yes, this is a pain, but it is better than trying to read googledegobble. At 11:51 PM 1/24/2013, Bill Gosper wrote: >Typed without linebreaks as an email experiment. I normally manually >linebreak, much to the puzzlement of of the kids, and my own frustration, >when GMail or something inserts additional breaks, creating a bunch of one >or two word lines. Contrariwise, all my formatting often suddenly >disappears when I paste partial conversations from Roundcube into GMail, >much to the irritation of Warren. Why can't it leave my goddam formatting >alone?

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[math-fun] unclever wine rack
by Bill Gosper 25 Jan '13

25 Jan '13

A local restaurant offended my geometric sensibilities with wine racks in the shape of squares quartered by diagonals into isosceles right triangles only large enough for five bottles, as in the N=5 example in http://hydra.nat.uni-magdeburg.de/packing/crt/d1.html, whereas elongating the squares slightly (for which there was clearly room) would have accommodated 4*six bottles, i.e. two cases. What are the dimensions of the rectangle of minimal area into which 24 unit disks can be packed disjoint from the diagonals? --rwg Typed without linebreaks as an email experiment. I normally manually linebreak, much to the puzzlement of of the kids, and my own frustration, when GMail or something inserts additional breaks, creating a bunch of one or two word lines. Contrariwise, all my formatting often suddenly disappears when I paste partial conversations from Roundcube into GMail, much to the irritation of Warren. Why can't it leave my goddam formatting alone?

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[math-fun] 3D-printed Mobius house
by Henry Baker 24 Jan '13

24 Jan '13

FYI -- If I had a 3D printer this big, I'd print something that couldn't be built any other way -- e.g., some sort of fractal structure. http://www.latimes.com/business/technology/la-fi-tn-landscape-house-2013012… Dutch architect plans world's first 3-D-printed building By Deborah Netburn 1:35 PM PST, January 21, 2013 Can you program a 3-D printer to build an entire building? Architect Janjaap Ruijssenaars wants to try. The Dutch architect has laid out plans for Landscape House -- a structure that looks like a Mobius strip or "one surface folded over into an endless band," as he describes it. To build it, he plans to use a 3-D printer called D-Shape that will lay down thin layers of sand that combine with a bonding agent to create a material that is reportedly akin to marble. Ruijssenaars has a few partners joining him on this strange house printing journey. To design the home he worked with Rinus Roelofs, a sculptor and mathematician. To build it, he will work with Enrico Dini, the large scale 3-D printing expert who invented the D-Shape printer. If you are imagining a giant house-sized printer slowly but surely building a house layer by layer, then you don't quite have it right. The Landscape House will be printed in chunks 6 meters by 9 meters (about 20 feet by 30 feet). Each structure will be built from the bottom up, in a series of 5 mm layers of sand deposit. When the building is done, workers will brush away the loose sand to reveal the bonded sand structure underneath. As 3-D printing is still a pretty new process, the structure will still have some concrete and fiberglass reinforcements. The BBC reports that the cost of the building will be $5 million to $6 million, and Ruijssenaars is hoping to have it finished by the end of 2014. To see the D-Shape in action and learn more about the inventor, check out the video below. http://www.youtube.com/watch?v=RYaRUVTwIVc

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[math-fun] Shakespeare's sonnets encoded in DNA
by Henry Baker 24 Jan '13

24 Jan '13

FYI -- Forget eBooks, throw out the Kindles; dnaBooks are here. It won't be long before a YouTube video's "going viral" will literally be "going viral" -- you'll "catch" the video, along with the common cold, and only be protected from it by next year's flu vaccine ! http://www.guardian.co.uk/science/2013/jan/23/shakespeare-sonnets-encoded-d… Shakespeare's sonnets encoded in DNA All 154 Shakespeare sonnets have been spelled out in DNA to demonstrate the vast potential of genetic data storage Ian Sample, science correspondent The Guardian, Wednesday 23 January 2013 14.21 EST His words have touched the lovelorn and been pored over by brooding teenagers for more than four hundred years, but now some of the most romantic poems ever penned have been written into the code of life. The entire collection of Shakespeare's 154 sonnets has been spelled out in DNA by scientists in Cambridge to demonstrate the vast potential of genetic storage. Huge quantities of information could be written into specks of DNA and archived for tens of thousands of years, the researchers claim. Alongside the Bard's sonnets, the scientists made strands of DNA that stored part of an audio file of Martin Luther King's 1963 speech "I have a dream", and the seminal research paper that first described the double helical nature of DNA by Francis Crick and James Watson, a decade earlier. Written in DNA, one of Shakespeare's sonnets weighs 0.3 millionths of a millionth of a gram. One gram of DNA could hold as much information as more than a million CDs, the researchers said. Nick Goldman and Ewan Birney at the European Bioinformatics Institute in Hinxton, near Cambridge, came up with the idea in a pub in Hamburg. They wondered what alternatives might exist to the expensive hard disks and magnetic tapes used to store the growing datasets that are becoming ever more common in biology. They knew that DNA was an incredibly efficient and compact way to store information, and set about devising a way to turn the molecules into digital memory: capable of encoding the 1s and 0s used to store words, images, music and video on computers. "We wrote on napkins and sketched out details, and realised we could probably do this," said Goldman. The scientists developed a code that used the four molecular letters or "bases" of genetic material Â known as G, T, C and A Â to store information. Digital files store data as strings of 1s and 0s. The Cambridge team's code turns every block of eight numbers in a digital code into five letters of DNA. For example, the eight digit binary code for the letter "T" becomes TAGAT. To store words, the scientists simply run the strands of five DNA letters together. So the first word in "Thou art more lovely and more temperate" from Shakespeare's sonnet 18, becomes TAGATGTGTACAGACTACGC. To test the procedure, Goldman and Birney converted the sonnets, Martin Luther King's speech, and the Watson and Crick paper into their new DNA code and emailed it to a US company called Agilent, which makes physical strands of DNA commercially for researchers. Several weeks later, the company returned a tiny test tube to the scientists. It contained a speck of DNA that encoded all the information they had sent. To make sure the DNA stored the information correctly, the Cambridge scientists mixed it into a solution and ran it through a gene sequencing machine. From that, they were able to read the complete files again, according to a report in Nature. A similar feat was achieved by the Harvard geneticist, George Church, last year. He encoded a copy of his book Regenesis, 11 images, and a computer program in DNA. The Cambridge work differs in how it corrects for spelling mistakes made when the DNA is either written, or read out at the other end. Each "word" of DNA code is written in four different ways, and there are millions of copies of each of these. Any mistakes in the DNA are likely to affect only a minority of the strands of code, and these can be spotted by comparing them. "One of the great properties of DNA is that you don't need any energy to store it. You keep it cold, dry and dark, and it lasts for a very long time. We know that because we routinely sequence woolly mammoth DNA that is kept by chance in those sorts of conditions," said Birney. The high cost of making DNA today means genetic storage in biological hard drives will not be practical for a long time. But Birney said that another 100-fold drop in the cost of DNA sequencing, which has already happened in the past decade, makes DNA storage economic for information that has to be archived for more than 50 years. Asked whether the DNA might pose a danger to health, if it found its way into a person or other animal, Goldman said: "The DNA we've created can't be incorporated accidentally into a genome, it uses a completely different code to that used by the cells of living bodies. If you did end up with any of this DNA inside you it would just be degraded and disposed of."

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Re: [math-fun] Excellent video lecture of classical orbit problems
by Henry Baker 24 Jan '13

24 Jan '13

The cool thing about this video for me was the visualization of these equi-energy "tubes" that allow transfer of bodies to a large number of places in the solar system consistent with that amount of energy. For planetary travel, these "tubes" are the space equivalent of _rivers_ and _sea lanes_/_trade winds_ that enabled millennia of early commerce on the Earth's surface. Just as the West Coast is receiving debris from Japan many, many months after the tsunami, the Earth is receiving debris from Mars, many, many years after some collision with Mars kicked this debris up into space. I would imagine that analogous "space tubes" connect our Sun with nearby stars in our galaxy. These tubes would provide a mechanism for transporting some small amounts of material over the billions of years of the Solar System's existence. I presume that every planetary system has ejected 1 or more significant sized planet that is free to travel these tubes and cause havoc in some other planetary system millions of years later. At 07:15 PM 1/23/2013, Fred lunnon wrote: > I watched this from start to finish in one sitting --- unput-downable! > > He just slipped this in briefly towards the end, but it seemed potentially >significant to me: in a dust cloud, dissipation causes (non-escaping) >particles to congregate in stable "torus" islands. If I've undertood this >correctly, it implies that once a system of two massive bodies has been >established, then the formation of a (coarsely) determined planetary system >is guaranteed within a relatively small timescale. > > Or maybe this is already well-known, and I just hadn't caught up ... > >Fred Lunnon > >On 1/23/13, Henry Baker <hbaker1(a)pipeline.com> wrote: >> FYI -- Talks about zero/low energy orbit transfers, potential >> Earth-colliding asteroids, ability of Mars ejecta to reach Earth, etc. >> >> The Interplanetary Transport Network: Mapping Chaotic Motion Through the >> Solar System, November 2008. Zurich Physics Colloquium. >> >> Shane Ross >> >> 55 minutes, 144MB download >> >> http://www2.esm.vt.edu/~sdross/movies/ross-zurich-2008.mov >> >> Free book on this topic: >> >> Dynamical Systems, the Three-Body Problem and Space Mission Design >> >> W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross >> >> Free online Copy >> >> 312 pages, with 128 illustrations; 16MB download >> >> http://www2.esm.vt.edu/~sdross/books/KoLoMaRo_DMissionBk.pdf >> >> Shane Ross web page: >> >> http://www.shaneross.com/

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[math-fun] Excellent video lecture of classical orbit problems
by Henry Baker 24 Jan '13

24 Jan '13

FYI -- Talks about zero/low energy orbit transfers, potential Earth-colliding asteroids, ability of Mars ejecta to reach Earth, etc. The Interplanetary Transport Network: Mapping Chaotic Motion Through the Solar System, November 2008. Zurich Physics Colloquium. Shane Ross 55 minutes, 144MB download http://www2.esm.vt.edu/~sdross/movies/ross-zurich-2008.mov Free book on this topic: Dynamical Systems, the Three-Body Problem and Space Mission Design W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross Free online Copy 312 pages, with 128 illustrations; 16MB download http://www2.esm.vt.edu/~sdross/books/KoLoMaRo_DMissionBk.pdf Shane Ross web page: http://www.shaneross.com/

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[math-fun] ISS Longeron Challenge
by Eric Angelini 23 Jan '13

23 Jan '13

Any taker on math-fun? http://community.topcoder.com/tc?module=MatchDetails&rd=15520 Best, É.

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[math-fun] rounded tetrahedron
by Bill Gosper 23 Jan '13

23 Jan '13

Yow, we didn't know about this! Not even the revolved Reuleaux. MoMath neither? Karzes>I wonder if Meissner tetrahedra (true constant width) would work better or worse than Reuleaux tetrahedra (approximate constant width) for this purpose. Tom ----------- Better: Presumably, a flat plate resting on the slightly bogus Reuleaux tetrahedron will have a small but finite angle of repose. Worse: If we round just one edge of a face on which the solid rests, it presumably will roll onto the adjacent face after < 60° tilt. But then it could pivot on that face and stagger back onto the previous one, etc., but, Better: because one of the Meissners has a face with three sharp edges and an apparently lower center of gravity, with presumably > 60° repose, if placed carefully. Actually, the abovementioned staggering wouldn't be necessary--once over an edge it would run away, under plausible scenarios of rolling friction and atmospheric viscosity. Tom, thanks for the wakeup! So the Meissner is really a rounded HEPtahedron. Here <http://gosper.org/roundtet.png>'s a rounded tetrahedron (monohedron?), unlikely to be constant width, with an extremely simple formula. --rwg Bill Gosper writes: > MLB> > > And what exactly does "smooth" buy us? Let's just ask instead: how would we > quadrangulate a rounded tetrahedron? > ------ > I nearly slid through a stopsign recently. It was on a sharp downgrade, > preceded by gravel washed off a hillside. Had the gravel been perfectly > spherical, I wouldn't even have slowed down. Except spherical gravel > would have rolled away. What about Reuleaux tetrahedra > (http://www.youtube.com/watch?v=jK7xPo1YXzY 3:18)? Neil 3D printed > a lovely one, ~1.5", and then split for CES w/o photographing it. > It's eerie to roll a book over. Why aren't they sold > at science museum gift shops? But would one stay put on a hill? > Neil claims, with sufficient friction, > an amazing 60°! They're much less round than you might think. > This has 007esque possibilities, not just for foot chases and > booby-traps. Imagine pursuing Bond on a winding road where he > releases a few pounds of Reuleaux gravel. You say > http://www.zombiesurvivalwiki.com/thread/3341691/Liquid+Banana+Peel+-+Make+… > is cheaper? OK, but it leaves a residue. For the perfect crime, use > dry ice Reuleaux gravel. > --rwg > http://gosper.org/reuleauxtet.png

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[math-fun] 3D printers for very light telescope mirrors ?
by Henry Baker 23 Jan '13

23 Jan '13

I was watching a video about new NASA space telescopes & how light the mirror assembly had to be (one of them is made of beryllium (!). One of the problems of any large telescope is how to build a mirror that is a very rigid structure, but also very light. Ignoring the problem of "active mirrors" for ground-based telescopes for the moment, isn't there some _fractal_ structure which can be both extremely light and yet extremely rigid that could be built using a 3D printer? I'm assuming that the face of the mirror is still a paraboloid, but the structure behind it has to be rigid & light, so that it can optimally resist deformation under gravity at a wide variety of angles. Just as important as the mirror itself is the rigidity of the structure holding the sensor (nowadays almost always a silicon chip). I would imagine that small versions of such structures could be built out of plastic at home using hobbyist 3D printers.

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[math-fun] Jeanine Mosely's snowflake sponge
by Michael Beeler 23 Jan '13

23 Jan '13

... made of ~49000 business cards. Neat! Congratulations! http://www.nytimes.com/2013/01/22/science/usc-exhibit-shows-fractals-built-…

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