May 2016 - mathfun@mailman.xmission.com

[math-fun] 3D printing puzzle
by Henry Baker 27 May '16

27 May '16

People are using 3D printers more & more for prototyping. I received a small electronic gizmo which plugs into a USB port whose plastic case was 3D printed. The problem is, the plastic case keeps falling apart, due to the relatively poor tolerances of current gen consumer 3D printers. So... The challenge is to come up with a way to print a little rectangular plastic box -- probably in 2 pieces -- that can be put together in such a way that it won't fall apart under normal handling (e.g., carrying it in your pocket banging up against your house keys), but can still be easily disassembled w/o any special tools, screws, etc. Note that current 3D printers have the following characteristics: * the plastic isn't very strong and isn't very flexible, so "fingers" that interlace may be too weak and may easily break off. * the plastic deforms slightly during printing, so registration isn't terribly good. * the resolution in different dimensions is different, so the tolerances have to be quite wide. If printing the box in 2 pieces won't produce a satisfactory answer, how about 3 pieces?

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Re: [math-fun] 3D printing puzzle
by Bill Gosper 27 May '16

27 May '16

Allan, you raise an excellent point. What holds these damned things together? Here's Rohan holding up a tubecube: gosper.org/Photo on 4-21-16 at 8.01 AM.jpg ,which he's convinced me comes right apart if all six [s simultaneously depart radially. And presumably, 3/4 of an octopus could slap it right back together. Admittedly, with wear it's getting a bit delicate. If I build another, it will have pairs of subtle, diamond shaped ridges in the middle of the long sides, to provide detents. Rohan: with an infinite Young's modulus, would these detents render it inseparable? Yet it's amazing how well simple friction facilitates secure but removable lids on jars and bottles, e.g. (Although I do notice drugstore prescription bottles now having detents.) --rwg And for centuries we've have corks securing wine bottles, probably down to the molecule. Note added in 24 proof, gosper.org/IMG_0204.JPG is now so worn that it flies apart with the slightest twirl. But the uninitiated never manage to pull it open. On 2016-05-27 12:34, Allan Wechsler wrote: > I think I am having trouble with the desiderata for this problem. If we are > not allowed to depend on friction, then the "assembly" path through > configuration-space can certainly be time-reversed to provide a > "disassembly" path, which will make the box liable to wiggle apart. Are > spring-snap fasteners of any kind allowed? I would think all of these would > tend to be a bit fragile. > > On Fri, May 27, 2016 at 3:19 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> Dear Joerg: >> >> I appreciate the offer, but I didn't design the box & don't have access to >> the STL file. >> >> I know the fellow who did, but I don't think that you want to do all of >> his production! :-) >> >> I was just trying to think of all the cool 3D puzzles I've seen in my life >> -- some of whom >> were made out of wood -- and try to recall if any of them would fit this >> particular bill. >> >> About the only thing I've thought of so far is a cylindrical device made >> out of two >> (identical) helical pieces of plastic that screw together; think of a DNA >> double helix. >> >> This shape more-or-less works for for a USB device, because the connector >> is a bit boxy >> anyway. >> >> At 11:03 AM 5/27/2016, Joerg Arndt wrote: >> >* Henry Baker <hbaker1(a)pipeline.com> [May 27. 2016 18:43]: >> >> People are using 3D printers more & more for prototyping. >> >> >> >> I received a small electronic gizmo which plugs into a USB port whose >> plastic case was 3D printed. >> >> >> >> The problem is, the plastic case keeps falling apart, due to the >> relatively poor tolerances of current gen consumer 3D printers. >> > >> >It seems you want something for actual use. Hence no PLA, instead >> >use ABS. If a consumer model is used, the operator will need some >> >skill (and quite possibly luck). >> > >> >ABS prints tend to warp, especially with cheaper printers. >> > >> >If you can have what you want made from a more expensive printer your >> >chances are much better, the operators will know very well what to do >> >for every requirement (my Uni bought one for 750 K Euro recently, they >> >had to take the wall out of the room to deliver it with a crane; that >> >one can do metal (sinter) prints with close to no restrictions). >> > >> >Alternatively, send me the STL file and I'll talk to the guys that >> >have bought a very decent printer that is good with ABS. >> >Payment is beer (this is Bavaria), I'll take care of that. >> > >> >Mit besten Gruessen, Joerg Arndt >> > >> >> So... >> >> >> >> The challenge is to come up with a way to print a little rectangular >> plastic box -- probably in 2 pieces -- that can be put together in such a >> way that it won't fall apart under normal handling (e.g., carrying it in >> your pocket banging up against your house keys), but can still be easily >> disassembled w/o any special tools, screws, etc. >> >> >> >> Note that current 3D printers have the following characteristics: >> >> >> >> * the plastic isn't very strong and isn't very flexible, so "fingers" >> that interlace may be too weak and may easily break off. >> >> >> >> * the plastic deforms slightly during printing, so registration isn't >> terribly good. >> >> >> >> * the resolution in different dimensions is different, so the >> tolerances have to be quite wide. >> >> >> >> If printing the box in 2 pieces won't produce a satisfactory answer, >> how about 3 pieces? >> >>

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Re: [math-fun] 3D printing puzzle
by Henry Baker 27 May '16

27 May '16

Where's the fun in using Shapeways? I was trying to turn this tolerance constraint into an interesting problem. Given the need for *little boxes* down through the ages -- e.g., for snuff, for cosmetics, etc. -- there have been all sorts of solutions to this problem. E.g., the Edo Japanese had their "Inro" boxes, which are pulled together with bits of string, and can sometimes be fabulously decorated: https://en.wikipedia.org/wiki/Inro One could easily make a miniature inro box for a USB device from relatively poor tolerance pieces. At 12:34 PM 5/27/2016, Bill Gosper wrote: >Henry, you've been cr@pped on. 3D printing is way better than >that. Shapeways (et al) will make stuff out of almost anything, >to almost any desired tolerance.

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Re: [math-fun] 3D printing puzzle
by Bill Gosper 27 May '16

27 May '16

On 2016-05-27 10:26, Fred Lunnon wrote: > I expect RWG can come up with something which will explode on command. > But it might take a fortnight to reassemble ... WFL > > > > On 5/27/16, Henry Baker <hbaker1(a)pipeline.com> wrote: >> People are using 3D printers more & more for prototyping. >> >> I received a small electronic gizmo which plugs into a USB port whose >> plastic case was 3D printed. >> >> The problem is, the plastic case keeps falling apart, due to the relatively >> poor tolerances of current gen consumer 3D printers. >> >> So... >> >> The challenge is to come up with a way to print a little rectangular plastic >> box -- probably in 2 pieces -- that can be put together in such a way that >> it won't fall apart under normal handling (e.g., carrying it in your pocket >> banging up against your house keys), but can still be easily disassembled >> w/o any special tools, screws, etc. >> >> Note that current 3D printers have the following characteristics: >> >> * the plastic isn't very strong and isn't very flexible, so "fingers" that >> interlace may be too weak and may easily break off. >> >> * the plastic deforms slightly during printing, so registration isn't >> terribly good. >> >> * the resolution in different dimensions is different, so the tolerances >> have to be quite wide. >> >> If printing the box in 2 pieces won't produce a satisfactory answer, how >> about 3 pieces? >> I expect Fred refers to https://www.youtube.com/watch?v=pvT5ySMnO8U which NeilB printed in ABS several years ago on his homebuilt (which you can hear running in the background.). Note adequate mechanical strength and accuracy. Henry, you've been cr@pped on. 3D printing is way better than that. Shapeways (et al) will make stuff out of almost anything, to almost any desired tolerance. (For a price.) These next two(?) are sintered nylon: gosper.org/IMG_0204.JPG gosper.org/tubecube1.jpg ("strong and flexible plastic") How about a steel-copper mix? https://www.bathsheba.com/math/klein/klein_Abeer.jpg Or bronze: https://www.youtube.com/watch?v=LGUfgplJRSc --rwg

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[math-fun] Binary number divisible by 3? (was Re: FW: squares beginning with n)
by Keith F. Lynch 27 May '16

27 May '16

Dan Asimov <dasimov(a)earthlink.net> wrote: > Zak, good question: Is there a quick way to detect multiples > of 3 expressed in base 2 ??? Replace any pairs of 1s that have an even number (possibly 0) of 0s between them and that have no other digits between them, with 0s. For instance 11->00, 1001->0000, 100001->00000. Repeat the above as many times as possible. Then discard any remaining 1s three at a time. The number of 1s left will be the original number's remainder when divided by 3. Examples: 2015: 11111011111 -> 11111011100 -> 11111010000 -> 11100010000 -> 10000010000. Two 1s left, so its 3-remainder is 2. 2016: 11111100000 -> 11110000000 -> 11000000000 -> 0. Divisible by 3. 2017: 11111100001 -> 11110000001 -> 11000000001 -> 1. One 1 left, so its 3-remainder is 1.

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Re: [math-fun] FW: squares beginning with n
by Bill Gosper 27 May '16

27 May '16

On 2016-05-25 06:41, Marc LeBrun wrote: >>="Joerg Arndt" <arndt(a)jjj.de> >> For every base b and every (tentative) divisor d one can obtain a >> periodic sequence of weights such that the weighted sum of digits >> tells whether a base-b number is divisible by d. > > Yes, I recall working out a similar thing some years ago, and being amused > that one could reasonably easily mentally test for divisibility by, say, 17 > or 19 (which may come in handy for factoring the number on my alarm clock). > > As a kid I encountered "The Trachtenberg Method of Speed Mathematics" which > espouses a bunch of special-case methods for rapidly multiplying by specific > small d. The divisibility tests here are sort of related. > > It's kind of interesting that this weighted-summing works LSB-to-MSB, the > opposite of naïve long division. As I think ACW mentioned long ago, base 10 mod 7 works LSD-to-MSD-to-LSD: First, convert to base 100 (LSD-to-MSD), optionally reducing the bidigits mod 7. Then MSD-to-LSD, double what you have and add the next digit, again mod 7 ad libitum. E.g., 2016 -> 40+16 -> 5+2 -> 0 Of course you can do 7, 11, and 13 simultaneously using base 1000 instead of 100, and left-to-right subtracting what you have from the next tridigit. This gets you mod 1001. So all we need is a slick three digits mod 13. --rwg

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[math-fun] German is easier than I thought it was
by Robert Baillie 26 May '16

26 May '16

I ran across this while going through some old papers. It was the sign on the door to the Â“Machine RoomÂ” where the mainframe was housed. I thought others might enjoy it, too! ACHTUNG Alles Lookenspeeper Das computenmachine is nicht fur gefingerpoken und mittengraben. Ist easy schnappen der springenwerk, blowenfusen, und poppencorken mit spitzensparken. Ist nicht fur gewerken by das dummkopfen. Das rubbernecken sightseeren keepen hands in das pokets--relaxen und watch das blinkenlights.

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Re: [math-fun] German is easier than I thought it was
by Jim Gillogly 26 May '16

26 May '16

That sign also graced the RAND Corporation basement room where our vacuum-tube Johnniac lived circa 1965, when I first learned to program using the JOSS on-line system. Those were the days! -- Jim Gillogly

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Re: [math-fun] German is easier than I thought it was
by Henry Baker 26 May '16

26 May '16

Yes, that sign was on the "machine room" in the company where I worked, right next to the collection of dead squirrels who had given their lives in a vain attempt to sabotage the building's electrical power supply. At 09:09 AM 5/26/2016, Allan Wechsler wrote: >Versions of this go back to the late sixties, at least. > >On Thu, May 26, 2016 at 11:03 AM, Robert Baillie <rjbaillie(a)frii.com> wrote: >> I ran across this while going through some old papers. It was the sign on >> the door to the "Machine Room" where the mainframe was housed. I thought >> others might enjoy it, too! >> >> ACHTUNG >> Alles Lookenspeeper >> >> Das computenmachine is nicht fur gefingerpoken und mittengraben. Ist easy >> schnappen der springenwerk, blowenfusen, und poppencorken mit >> spitzensparken. Ist nicht fur gewerken by das dummkopfen. Das rubbernecken >> sightseeren keepen hands in das pokets--relaxen und watch das blinkenlights.

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[math-fun] about Ramanujan
by Simon Plouffe 26 May '16

26 May '16

Hello, the film : The man who knew infinity went out, with Jeremy Irons as G.H. Hardy. based on the novel I presume ? That version of the life of Ramanujan seems good, I saw one made in India about S.Ramanujan, my god it was bad, I don't remember the title, I did not finished the film , it was too bad , it did not resemble the real thing at all. but that one with Irons seems more credible 7.7 / 10 on IMDB scale. here is the film : http://www.imdb.com/title/tt0787524/ cheers and best regards, Simon Plouffe

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