January 2015 - mathfun@mailman.xmission.com

[math-fun] In https://twitter.com/wolframtap/status/522518755168243712 , profligate pleonast
by Bill Gosper 09 Feb '15

09 Feb '15

NeilB tweeted three superfluous characters: (*primes*)d[n_,t_,k_]:=If[k<1,Boole[n<1],If[t>n,0,d[n-t,0,k-1]+d[n,1/2+t+Sqrt[2t+1/4],k]]];2Select[Range[99],2#+2==d[#,0,4]&]+1 Can you find them? —rwg

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[math-fun] Unique factorization (connection to music?) question
by Warren D Smith 05 Feb '15

05 Feb '15

>Victor Miller victorsmiller at gmail.com >According to SAGE the field Q(2^{1/12}) has class number 1, and so does >have unique factorization. In addition Z[2^{1/12}] is the maximal order in >this field. --so: for which N does Q(2^{1/N}) have class number 1? http://oeis.org/A005848 = {1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 24, 25, 27, 28, 32, 33, 35, 36, 40, 44, 45, 48, 60, 84} claims to answer the same question for Q(Nth root of unity) duplicating the Main Theorem of J. Myron Masley and Hugh L. Montgomery: Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976) 248-256 which shows that all such N obey N<=84 and gives the full list. Amazingly enough, all the historically-used music-scale sizes {4,5,6,7,8,12} happen to be on this list (asterisk: M&M explain that if k is odd and on their list, then 2k automatically is also, so therefore they omit mentioning all 2k with k odd). Which actually is not so amazing since ALL numbers 1-12 are on the M&M list.

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[math-fun] Microwave ovens
by James Propp 02 Feb '15

02 Feb '15

Why do microwave ovens alternate between rotating the food-carousel clockwise and rotating it counterclockwise (or, as the Brits would say, anticlockwise)? Jim Propp

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[math-fun] Fwd: Big Splat theory
by Bill Gosper 31 Jan '15

31 Jan '15

On 2014-01-11 19:37, James Propp wrote: > Has anyone ever proposed in the Annals of Improbable Research or a similar > venue that, in addition to undergoing periodic reversals of its magnetic > field, Earth is also subject to occasional short-lasting reversals of its > gravitational field? > Botannical evidence: gosper.org/IMG_0323.JPG > Such a phenomenon would handily explain selective extinction of megafauna: > a mouse could survive an upward fall for five seconds followed by a > downward fall for five seconds followed by an extreme deceleration, but a > mastodon would not fare as well. :-) > > Jim Propp Maybe it was a gravity wave from a thud like the following, or maybe the following already happened. -------- Original Message -------- Subject: [math-fun] Humongous Thud coming Date: 2015-01-07 12:57 From: Warren D Smith <warren.wds(a)gmail.com> To: math-fun(a)mailman.xmission.com Reply-To: math-fun <math-fun(a)mailman.xmission.com> http://www.nytimes.com/2015/01/08/science/in-a-far-off-galaxy-2-black-holes… https://www.caltech.edu/news/unusual-light-signal-yields-clues-about-elusiv… Matthew J. Graham, S. G. Djorgovski, Daniel Stern, Eilat Glikman, Andrew J. Drake, Ashish A. Mahabal, Ciro Donalek, Steve Larson, Eric Christensen: A possible close supermassive black-hole binary in a quasar with optical periodicity, NATURE Wednesday 7 January 2015 http://www.nature.com/nature/journal/vaop/ncurrent/full/nature14143.html If they are right, then two supermassive black holes are in an orbit the size of the solar system, and are going to merge soon (within 1 million years) due to loss of energy from gravity waves it is radiating. The resulting thud is going to be far bigger than anything humanity has ever observed. Matthew J. Graham, S. G. Djorgovski, Daniel Stern, Eilat Glikman, Andrew J. Drake, Ashish A. Mahabal, Ciro Donalek, Steve Larson, Eric Christensen, DOI:10.1038/nature14143

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[math-fun] Laser inventor Charles Townes 1915-2015
by Eugene Salamin 29 Jan '15

29 Jan '15

http://www.osa.org/en-us/about_osa/newsroom/obituaries/charles_townes/?utm_… -- Gene

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Re: [math-fun] how much life lost by being off the optimum weight curve?
by Henry Baker 27 Jan '15

27 Jan '15

Warren: It would be interesting to try this "Eureqa" algorithm on your data. You can download & try it out for free. http://www.nutonian.com/products/eureqa/ At 11:29 AM 1/26/2015, Warren D Smith wrote: >I do not have that data, but presumably the life insurance companies that >produced the "optimum weight range" data did. I just parasited off MetLife. > >Here are some other life insurance co tables somebody collected, I have no idea what if >any science is behind them... but i we optimistically assume they knew >what they were doing, then the extra premiums you had to pay from being off curve, translate into >reduced lifespan in the obvious way...: > >http://www.victorson.com/pdf/LTC/HeightandWeightChart[1].pdf

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Re: [math-fun] deflategate
by Henry Baker 27 Jan '15

27 Jan '15

This whole "deflategate" thing would be a wonderful high school science project. At 08:09 AM 1/27/2015, rcs(a)xmission.com wrote: >Won't there be condensation inside the ball? >Is this normal? >----- >Quoting Mike Speciner <ms(a)alum.mit.edu>: > >>A quick calculation of decrease in pressure caused by decrease in temperature... >>Assumptions: >>(1) volume unchanged [rigid container] >>(2) sealed container >>(3) initial pressure 12.5 psi at 24C, 100% humidity air >>(4) except for H2O component, assume ideal gas >>(5) final pressure calculated at 6C >>(6) pressures above are relative to atmospheric pressure, 14.7 psi >> >>Calculation: >>partial pressure of H2O at 24C is .433 psi; partial pressure of >>remaining gas is thus 26.77 psi >>partial pressure of H2O at 6C is .135 psi; partial pressure of >>remaining gas is 279/297*26.77psi = 25.15psi >>Total pressure at 6C is then 25.15+.135 psi = 25.29 psi (10.6 psi >>relative to atmospheric pressure)

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[math-fun] deflategate
by Mike Speciner 27 Jan '15

27 Jan '15

A quick calculation of decrease in pressure caused by decrease in temperature... Assumptions: (1) volume unchanged [rigid container] (2) sealed container (3) initial pressure 12.5 psi at 24C, 100% humidity air (4) except for H2O component, assume ideal gas (5) final pressure calculated at 6C (6) pressures above are relative to atmospheric pressure, 14.7 psi Calculation: partial pressure of H2O at 24C is .433 psi; partial pressure of remaining gas is thus 26.77 psi partial pressure of H2O at 6C is .135 psi; partial pressure of remaining gas is 279/297*26.77psi = 25.15psi Total pressure at 6C is then 25.15+.135 psi = 25.29 psi (10.6 psi relative to atmospheric pressure)

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[math-fun] Let it snow
by James Propp 27 Jan '15

27 Jan '15

What do you all make of the precipitation forecast at http://forecast.io for the Boston area? Does "0.2 in/hr" mean one-fifth of an inch per hour? It seems to me, given the severity of the current blizzard, they must mean something closer to two inches per hour. I made an attempt at visually integrating the curve they show, and it yielded a total snowfall of 3 inches for the coming week. That can't be what they mean. Did I mis-integrate? Or have they mis-labeled their vertical axis? Jim Propp

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[math-fun] how much life lost by being off the optimum weight curve?
by Warren D Smith 26 Jan '15

26 Jan '15

I do not have that data, but presumably the life insurance companies that produced the "optimum weight range" data did. I just parasited off MetLife. Here are some other life insurance co tables somebody collected, I have no idea what if any science is behind them... but i we optimistically assume they knew what they were doing, then the extra premiums you had to pay from being off curve, translate into reduced lifespan in the obvious way...: http://www.victorson.com/pdf/LTC/HeightandWeightChart[1].pdf

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