March 2018 - mathfun@mailman.xmission.com

[math-fun] Series puzzle
by Dan Asimov 10 Mar '18

10 Mar '18

A series puzzle that appeared a long time ago in a puzzle section of a math magazine is this nice one, that some recent math-fun posts reminded me of: PUZZLE: Given positive integers K and L, express in closed form the Sum_{0 <= n < oo} 1 / (Kn + L)! I've never tried to evaluate this if Kn + L is replaced by a quadratic or higher-degree integer polynomial in n. —Dan

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[math-fun] Bale problem's
by françois mendzina essomba2 10 Mar '18

10 Mar '18

Hello In an unfortunate attempt to solve zeta (2n + 1), I became interested in certain functions. I was able to find: cos (x / sqrt (2)) * cosh (x / sqrt (2)) = sum ((- 1) ^ n * x ^ (4 * n) / (4 * n)!,n=0..infinity) but I am lost to the next sum. sum ((- 1) ^ n * x ^ (3 * n) / (3 * n)!,n=0..infinity) = ??? Do you know the function returned by this sum? I just noticed that the solutions of the equation sum ((- 1) ^ n * x ^ (3 * n) / (3 * n)!,n=0..infinity) = 0 are substantially close to: (2 * n + 1) * Pi / sqrt (3) Is there more information on this?

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Re: [math-fun] Bale problem's
by W. Edwin Clark 10 Mar '18

10 Mar '18

On Sat, Mar 10, 2018 at 5:50 PM, françois mendzina essomba2 via math-fun < math-fun(a)mailman.xmission.com> wrote: > Hello > > In an unfortunate attempt to solve zeta (2n + 1), I became interested in > certain functions. > > I was able to find: > > cos (x / sqrt (2)) * cosh (x / sqrt (2)) = sum ((- 1) ^ n * x ^ (4 * n) / > (4 * n)!,n=0..infinity) > > but I am lost to the next sum. > > sum ((- 1) ^ n * x ^ (3 * n) / (3 * n)!,n=0..infinity) = ??? > > Do you know the function returned by this sum? > Maple gives: (1/3)*exp(-x)+(2/3)*exp((1/2)*x)*cos((1/2)*3^(1/2)*x)

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[math-fun] Mechanical models of long tail distributions?
by Henry Baker 10 Mar '18

10 Mar '18

We've all seen those balls-and-pegs mechanical models which produce good approximations to binomial distributions (and hence Gaussian distributions). Are there any simple mechanical models for Zipf's Law? Power law? Pareto distribution? Log-normal distributions? In particular, if one were trying to produce a power law distribution, it would be nice if it somehow involved the equivalent of a log-log plot (where the distribution becomes linear).

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Re: [math-fun] Set-theory symbols
by Guy Haworth 09 Mar '18

09 Mar '18

... to Paul Reiners .... No: not 'across the streets'. The Unicode Symbols have rooms in the Unicode Hotel. :-) G

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Re: [math-fun] Averaging functions on trees
by Dan Asimov 09 Mar '18

09 Mar '18

I am especially interested in trees but realized the question makes sense for any graph. I do mean undirected graphs, so the line << E is a subset of V x V - diagonal Should have read << E is a symmetric subset of V x V - diagonal. But I am surprised to hear that A^2n(f) (or A^(2n+1)(f)) might converge for *all* f. Can't I make f increase so fast in terms of distance from some fixed point P that A^(2n)(f)(P), say, gets arbitrarily large as n —> oo ? —Dan Andy Latto wrote: ----- On Sun, Mar 4, 2018 at 2:41 PM, Dan Asimov <dasimov(a)earthlink.net> wrote: > Let G be an infinite connected graph > > G = (V, E) > > where V is a countably infinite set and E is a subset of V x V - diagonal, You don't say whether (x, y) can be in E while (y, x) is not. Are you asking about directed or undirected graphs? The subject line refers to trees: did you intend to also specify the graph is acyclic? > > satisfying 1) and 2): > > ----- > 1) Every edge e in E has 2 endpoints, and any 2 vertices v,w in V bound > at most one edge. > > 2) If for any v in V, deg(v) denotes the number of edges v belongs to, > then for all v we have > > 2 <= deg(v) < oo. > ----- > Question: Which f in C approach a limit under iteration of A: > > lim A^n(f) = f^ > n—>oo > > for some f^ in C > ??? I don't have a proof yet, but I assuming we're talking about undirected graphs, I believe that this will converge for all f if G is not bipartite. If G is a bipartite graph, which includes all acyclic graphs, then I think that lim A^2n(f) = f^ n—>oo and lim A^(2n+1)(f) = f^ n—>oo Will always both exist, but will generally be different. -----

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Re: [math-fun] Getting ready to celebrate Pi Day?
by Bill Gosper 09 Mar '18

09 Mar '18

314 Circle Circle might be a good place to build a casino. --rwg -------- Original Message -------- Subject: Re: [math-fun] Getting ready to celebrate Pi Day? Date: 2018-03-09 12:33 From: Allan Wechsler <acwacw(a)gmail.com> To: math-fun <math-fun(a)mailman.xmission.com> Reply-To: math-fun <math-fun(a)mailman.xmission.com> There are several 314 Circle Rd addresses, apparently. On Fri, Mar 9, 2018 at 3:27 PM, Thane Plambeck <tplambeck(a)gmail.com> wrote: > Where to celebrate Pi Day? > > According to Google maps, the following five North America cities include a > building address at 314 Day Street: > > Moreno Valley, CA > San Francisco, CA > Winnipeg, Canada > Jackson, TN > Rolling Fork, MS > > I've been to two Pi Day parties at 314 Day St in San Francisco. I happen > to know the couple who live there. > > I'm not sure if 3141 or 3142 would be better in the conceivable 3100 block > addresses on Day Streets. > > On Fri, Mar 9, 2018 at 11:39 AM, Henry Baker <hbaker1(a)pipeline.com> wrote: > > > FYI -- Anyone here live in Seattle? > > > > https://www.lokokitchen.com > > > > https://www.instagram.com/lokokitchen/ > >

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[math-fun] Set-theory symbols
by Guy Haworth 09 Mar '18

09 Mar '18

The Unicode 'set intersection' symbol is U+2229 ... and for 'set union' is U+222A [i.e. 'next door']. There's a standard way of inserting Unicode characters into Word documents .... https://www.fileformat.info/tip/microsoft/enter_unicode.htm ... or pick these symbols out of 'Symbols' with 'Insert Symbol'. G

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[math-fun] Getting ready to celebrate Pi Day?
by Henry Baker 09 Mar '18

09 Mar '18

FYI -- Anyone here live in Seattle? https://www.lokokitchen.com https://www.instagram.com/lokokitchen/

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[math-fun] Good set-theory symbols
by James Propp 09 Mar '18

09 Mar '18

Anyone know of a good Unicode set-union symbol? I've been using ∩ for intersection and ∪ for union in Word documents. I like the former but I find the latter too elongated. I've checked a few places on the web but can't seem to find an upside-down ∩ . (Is there something that does for Unicode what detexify does for tex?) Thanks, Jim Propp

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