March 2018 - mathfun@mailman.xmission.com

Re: [math-fun] Brillouin zones
by Dan Asimov 08 Mar '18

08 Mar '18

This looks relevant: https://mathoverflow.net/questions/221636/limiting-shape-for-brillouin-zones —Dan Jim Propp wrote: >I’m imagining that the nth Brillouin zone, rescaled by sqrt(n), converges >to a circle in the Hausdorff metric. >On Thursday, March 8, 2018, Dan Asimov <dasimov(a)earthlink.net> wrote: > >> Jim Propp wrote: >> ----- >> Does the nth Brillouin zone converge in shape to a circle as n goes to >> infinity? >> ----- >> >> What kind of convergence? Maybe in the sense that the stairstep >> approximation converges to s diagonal line?

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Re: [math-fun] Brillouin zones
by Dan Asimov 08 Mar '18

08 Mar '18

Jim Propp wrote: ----- Does the nth Brillouin zone converge in shape to a circle as n goes to infinity? ----- What kind of convergence? Maybe in the sense that the stairstep approximation converges to s diagonal line? —Dan

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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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