November 2014 - mathfun@mailman.xmission.com

[math-fun] It was only a matter of time
by Bill Gosper 05 Nov '14

05 Nov '14

before they started 3D printing quinces. gosper.org/IMG_0274.JPG --rwg

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[math-fun] Diophantine
by David Wilson 04 Nov '14

04 Nov '14

a^2 - b^2 = c^2 - d^2 = e^2 - f^2 a^2 + b^2 = c^2 + f^2 = e^2 + d^2 Any solutions in nonzero integers?

2 2

[math-fun] Coffee and theorems
by Bill Gosper 04 Nov '14

04 Nov '14

HGB>Uh-oh. What's the Erdos # for "amphetamines" ? Zero. At 02:12 PM 11/3/2014, Allan Wechsler wrote: I thought ErdÅ‘s originally said "amphetamines". On Mon, Nov 3, 2014 at 5:04 PM, Dan Asimov <dasimov(a)earthlink.net> wrote: I've heard that this quote is due to Paul ErdÅ‘s. --Dan On Nov 3, 2014, at 1:40 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: "Mathematicians turn coffee into theorems." -- unknown ?? And who said: "A CS grad student is a machine for turning coffee into urine."? --rwg

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[math-fun] Kerr-boom?
by Henry Baker 04 Nov '14

04 Nov '14

What happens when 2 equal & oppositely-rotating black holes merge? I guess it would depend on the angle of the collision vector compared with the mutual axis of rotation, but no matter what the angle is, it would be interesting.

4 4

[math-fun] what happened when self-reference met philately?
by Alex Bellos 04 Nov '14

04 Nov '14

http://www.theguardian.com/science/alexs-adventures-in-numberland/2014/nov/…

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Re: [math-fun] Unconditionally stable nesting coffee cups?
by Henry Baker 03 Nov '14

03 Nov '14

Uh-oh. What's the Erdos # for "amphetamines" ? At 02:12 PM 11/3/2014, Allan Wechsler wrote: >I thought ErdÅs originally said "amphetamines". > >On Mon, Nov 3, 2014 at 5:04 PM, Dan Asimov <dasimov(a)earthlink.net> wrote: >> I've heard that this quote is due to Paul ErdÅs. >> > --Dan >> > > On Nov 3, 2014, at 1:40 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> > > "Mathematicians turn coffee into theorems." -- unknown ??

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Re: [math-fun] Unconditionally stable nesting coffee cups?
by Bill Gosper 03 Nov '14

03 Nov '14

On Mon, Nov 3, 2014 at 2:13 PM, Michael Greenwald <mbgreen(a)seas.upenn.edu> wrote: Must the base be larger than the top? Or would it suffice to have a small, very dense, heavy, weight located in the base (small = radius of the weight < radius of the base, heavy = comparably heavy to the weight of water when the cup is full)? Tungsten is pretty cheap and very dense, e.g. I got some 100g tungsten counterweights for $10 each. -- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com Amazingly cheap, given it's non-abundance. "This guidance uses the lifting force experienced by the aeroshell to "fly out" any detected error in range and thereby arrive at the targeted landing site. In order for the aeroshell to have lift, its center of mass is offset from the axial centerline that results in an off-center trim angle in atmospheric flight. This is accomplished by a series of ejectable ballast masses consisting of two 75 kg (165 lb) tungsten <http://en.wikipedia.org/wiki/Tungsten> weights that were jettisoned minutes before atmospheric entry.[134] <http://en.wikipedia.org/wiki/Mars_Science_Laboratory#cite_note-spaceflightn…> " http://en.wikipedia.org/wiki/Mars_Science_Laboratory Compared to the transportation costs, I guess it might as well have been solid gold. Alan Adler bought some W for Euler disks. Disappointing. Fun to fondle, though. --rwg

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Re: [math-fun] Unconditionally stable nesting coffee cups?
by Henry Baker 03 Nov '14

03 Nov '14

If I didn't care about handles, I could do the following: Take the letter M & take the surface of revolution through the vertical center axis. If the outer legs of the M are splayed out, then the M's can nest. The liquid is held in the inner "v" of the M. For a lower center of gravity, consider an M with a "U" shaped central portion. For suitable U shapes, they can nest. The result looks like many dog bowls, some of which can nest. Now weld a "logical not"-shaped handle to this dog dish. In order to nest with another of the same form, we need to rotate one so it doesn't hit the handle of the lower dish. We also need to cut a slot into the outer rim of the upper dish when the lower handle will fit. If we iterate this construct, we get dishes with handles & offset slots. Depending upon the depth of the nesting, we may need to introduce additional slots, although these additional slots don't have to be so deep, because they hit handles 1,2,3,... cups down in the stack. Depending upon the design, we can have >2 handles which double as "outriggers", or one handle + additional slots. The most symmetrical version would have 3 handles at 120-degree positions, and N cups would nest, where N depends upon the angular width of the handles. At 02:05 PM 11/3/2014, Mike Stay wrote: >You could use the usual truncated cone (bottom smaller than top) with >three legs coming off the rim to give it the stability you're looking for. > >On Mon, Nov 3, 2014 at 1:55 PM, Dave Dyer <ddyer(a)real-me.net> wrote: >> >> How about a conventionally shaped cup with a slight outward >> bevel, but with 3 handles that are long enough to touch the >> desk, and serve as outriggers.

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Re: [math-fun] Ménage primes
by Bill Gosper 03 Nov '14

03 Nov '14

On 2014-10-30 19:24, Adam P. Goucher wrote: > Here's a problem to be added to Ed Pegg's list of prize puzzles: find > another ménage prime. > > https://cp4space.wordpress.com/2014/10/31/menage-primes/ > > So far, only five such primes are known (although I haven't searched > beyond n = 10000): > > M(4) = 5 > M(5) = 13 > M(13) = 775596313 > M(53) = 567525075138663383127158192994765939404930668817780601409606090331861 > M(8645) = > 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> > Happy Halloween! > > > Sincerely, > > > Adam P. Goucher > A000179: 1, 0, 0, 1, 2, 13, 80, 579, 4738, 43387, 439792,... In[319]:= Table[Round[2*n/E^2*BesselK[n, 2]], {n, 9}] Out[319]= {0, 0, 1, 2, 13, 80, 579, 4738, 43387} BesselK!?! --rwg Hallowe'en: Yesterday, Jake's Pizza in Saratoga in the window had a certificate of approval from the Santa Clara County Board of Health. Inside: wall to wall spiders on massive fake webs.

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[math-fun] Recreational math in Lisbon, Jan 2015
by Thane Plambeck 02 Nov '14

02 Nov '14

Carlos Santos asked me to pass on a pointer to this recreational mathematics conference in Lisbon early next year. http://ludicum.org/ev/rm/15 -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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