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[math-fun] Brillouin zones
by James Propp 08 Mar '18

08 Mar '18

I just came across http://skepticsplay.blogspot.com/2011/10/lot-of-brillouin-zones.html Does anyone see how to prove that all the zones have the same area? Jim Propp

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[math-fun] International Women's Day
by françois mendzina essomba2 08 Mar '18

08 Mar '18

Hello... At his request, I sent the following lines to a friend sum(2^k*tan(2^k*x),k=0..n)=cot(x)-2^(n+1)*cot(2^(n+1)*x); sum(2^k*tanh(2^k*x),k=0..n)=-coth(x)+2^(n+1)*coth(2^(n+1)*x); tanh(2*x)=2/(coth(x)+2/(coth(x/2)+2/(coth(x/4)+2/(coth(x/8)+2/(coth(x/16)+2/(coth(x/32)+2/(coth(x/64)+2/(coth(x/128)+2/(coth(x/256)+2/cdots))))))))); tan(2*x)=2/(cot(x)-2/(cot(x/2)-2/(cot(x/4)-2/(cot(x/8)-2/(cot(x/16)-2/(cot(x/32)-2/(cot(x/64)-2/(cot(x/128)-2/(cot(x/256)-2/cdots))))))))); I do not know if she understood anything about it.finally she had a good time. FME...

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[math-fun] "What applications does that have?"
by Joerg Arndt 08 Mar '18

08 Mar '18

Anyone being annoyed by this question when you presented something you found beautiful in its own? I certainly have. Plus, being a bit diplomatically challenged (ask Neil!), I'd like to hear a way of answering that question without appearing to be rude. "I don't care one bit" does not work, as I verified empirically. Best regards, jj

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Re: [math-fun] "What applications does that have?"
by Hilarie Orman 08 Mar '18

08 Mar '18

> "My name is William Rowan Hamilton > I just invented the quaternion > It hasn't got an applicay-shee-yun > But just you wait, just you wait ..." 'enry 'iggins? I like Gosper's occasional cutting remark about some theorem being "at the top of the food chain". In my opinion, there is one example in mathematical music theory for determing n such that "chordality equals ordinality". Hum a few bars. Hilarie

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[math-fun] "Knightship detected (speed (sic) = 2,1c/6)" !!
by Bill Gosper 07 Mar '18

07 Mar '18

Our own Adam Goucher (building on work from our own Tom Rokicki) has found a Life pattern sought for 48 years! x = 31, y = 79, rule = B3/S23 25b2o$23bo2bo$22bo3bo$22b3o$17b4o6b2o$17b4o4b2obo$15b3o6bo4bo$15bo3b2o 4b4o$19b2o9bo$25bo3bo$15bo2b2o2b3o$14bo4bo7b2o$14b2obo$12bo6b2o$12bob 3ob2o$12bo2bo3b2o$14b2o2bobo$13bobobo2bo$11bo6b3o$11bo3bobobo$11bobob 2o$10b3o6bo2$9bo9bo$8bo6bo3bo$8b5o5bo$16b3o$13b2o$12bo2b3o$13bob3obo$ 13bo2bo3bo$9b3ob2o4bo$6b2o4bob4o$6b2o4b4obo$11bo$6b2o2bo$9b2o$5b5o$4b 2o$2bo6b3o$2bobo3bobo$3bo3bo3bo$6b2o3bo$b3obo6bo$b2o3bo3b2o$bo2bo2b4o$ 3bo3b2o$9bo$6bob2o$10bo$7b5o$6bo4bo$6b3ob3o$6b5obo$12bo$10bo$6b4o4bo$ 4b2ob4o$6bo4b3o$4bobo$2bo$2b2o2bo$3b3o$7b2o$bo5b3o$obo2b2o$obob3o2bo$ 2bo2bob2o$2o2bobo$3b2o$bo4b3o$bo4b3o$3o3b2o$2b2ob2o$4b2o$5bo2$5b2o$4bo ! (Amazing that Golly called it a knightship.) RKG: Tell JHC! --rwg (Rohan: Tnx for the headsup!)

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Re: [math-fun] "What applications does that have?"
by Hilarie Orman 06 Mar '18

06 Mar '18

Oops, not ordinality, but cardinality. Hilarie

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Re: [math-fun] "What applications does that have?"
by Dan Asimov 06 Mar '18

06 Mar '18

I don't think "annoyed" describes my reaction. But inevitably that question comes from non-mathematicians, and the puzzle is how best to answer. Especially when you're speaking to people who have not experienced the joy of beautiful math before. But it can be a great pleasure to introduce someone to beautiful math for the first time. If people have standard examples they like to use, or think would be good to use, as beautiful mathematics for beginners, what are they? —Dan ----- Anyone being annoyed by this question when you presented something you found beautiful in its own? I certainly have. Plus, being a bit diplomatically challenged (ask Neil!), I'd like to hear a way of answering that question without appearing to be rude. "I don't care one bit" does not work, as I verified empirically. -----

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Re: [math-fun] "What applications does that have?"
by Bill Gosper 06 Mar '18

06 Mar '18

Well, whoever said it (Faraday? Franklin? Both?), "What good is a newborn baby?" works for me. --rwg On 2018-03-06 11:36, W. Edwin Clark wrote: > You might say, "No, but someday you may tax it." ---as Faraday is supposed > to > have said to an English prime minister when he asked what the usefulness > of one of his > electromagnetic devices was. (Nice story but apparently never happened > <https://www.snopes.com/quotes/faraday.asp> .) > > > On Tue, Mar 6, 2018 at 1:04 PM, Joerg Arndt <arndt(a)jjj.de> wrote: > >> Anyone being annoyed by this question when you presented something you >> found beautiful in its own? I certainly have. Plus, being a bit >> diplomatically challenged (ask Neil!), I'd like to hear a way of >> answering that question without appearing to be rude. "I don't care >> one bit" does not work, as I verified empirically. >> >> Best regards, jj

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Re: [math-fun] SQRT occurring in inventory management optimization ?
by Henry Baker 06 Mar '18

06 Mar '18

Thanks! There appear to be many different SQRT examples in optimal inventory management, but the SQRT's seem to come from two different sources: fixed cost amortizations and random walks from statistical deviations in Gaussian/normal distributions. Here's the simplest example I can think of: withdrawing cash from an ATM machine. s is constant spend rate per year; s = total $ spent in one year. r is simple interest rate per year. A is ATM fee per withdrawal; A is independent of amount of cash withdrawn. C is the amount of cash withdrawn on each trip to the ATM. We want to find the optimal amount of cash C* to withdraw on each trip to the ATM. C* minimizes the total ATM fees in one year + total interest foregone in one year. Trips to the ATM in one year = s/C Total ATM fees in one year = A*(s/C) Mean amount of cash on hand = C/2 (spend rate is constant) Simple interest foregone in one year = r*(C/2) Total costs in one year: T = A*(s/C) + r*(C/2) dT/dC = -s*A/C^2 + r/2 = 0 Solving for C, we get C* = C = sqrt(2*s*A/r) Suppose A=$5, r=3%, s=$30/year, C*=$100. i.e., even though I spend only $30 cash per year, I'm still best off withdrawing $100 every trip to the ATM. #trips to the ATM in one year = 30/100 = .3 trips/year ATM costs per year = $5*0.3 = $1.50 Mean cash on hand = $50 Simple interest foregone per year = $50*3/100 = $1.50 So, with optimum cash withdrawal amounts, the ATM fees equal the interest foregone. https://en.wikipedia.org/wiki/Economic_order_quantity At 06:37 AM 3/6/2018, Seb Perez-D wrote: >Square roots do appear in optimal inventory >https://www.wiley.com/legacy/wileychi/waters/supp/Equations.pdf > >In particular (S,s) models >https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.24.1.183 > >Cheers, > >Seb > >On 5 March 2018 at 21:33, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> I seem to recall a classical inventory management problem whose optimum >> solution involves a sqrt function. >> >> Since I never took a Operations Research course, I think that this problem >> showed up in a calculus class & used Lagrange multipliers. >> >> But after Googling a while, I couldn't find it. >> >> Anyone here recall a similar problem?

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Re: [math-fun] Math-Fun topics
by Bill Gosper 06 Mar '18

06 Mar '18

Should be safe. Most of the antinukes have switched to you-know-what. Won't the next breakthrough be quantum computing? If it works. --rwg On 2018-03-02 09:44, Eugene Salamin via math-fun wrote: > Surely discussion of nuclear reactors should be an allowed math-fun topic. > > -- Gene > > > > On Friday, March 2, 2018, 9:28:38 AM PST, Richard Howard > <rich(a)richardehoward.com> wrote: > > Sorry about that--will do. > > There is the slight twist in that I was trying to respond to the issue of *new > technologies* that are down the road. > Leaving out geoengineering or pocket nuclear reactors and including Bitcoin > seems to be leaving the elephant in the living room from the "technology" > point of view. > > Adversarial AI is ok, though--right? > > --R > > On Fri, Mar 2, 2018 at 11:35 AM, <rcs(a)xmission.com> wrote: > >> We've had some new folks join us recently, >> who might be unaware of some of my arbitrary rules. >> >> The topics of politics and global warming are banned. >> >> Rich

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