December 2016 - mathfun@mailman.xmission.com

[math-fun] science museum has new math gallery (London)
by James Buddenhagen 19 Dec '16

19 Dec '16

see here: http://artdaily.com/news/92261/Maths-explored-in-new-Science-Museum-gallery…

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[math-fun] Variants of the Etch-a-Sketch
by James Propp 19 Dec '16

19 Dec '16

Has anyone made variants of the Etch-a-Sketch featuring knobs that allow other sorts of control (e.g., drawing a circular arc with a prescribed center)? Jim Propp

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Re: [math-fun] The difficulty of integration vs. the ease of differentiation
by Henry Baker 19 Dec '16

19 Dec '16

I was hinting at the fact that integrate(A(x)/B(x),x), where A(x), B(x) are polynomials in x, is quite easy when B(x) factors into linear factors; use partial fraction expansion. A lot of trig functions crop up when you are unable or unwilling to move into the complex domain and B(x) has quadratic factors. At 02:27 PM 12/16/2016, Fred Lunnon wrote: >Numerically speaking, integration is in contrast easier than differentiation ... WFL > >On 12/16/16, Henry Baker <hbaker1(a)pipeline.com> wrote: >> 2. Some closed form integrals may require polynomial root-finding (or root >> expressing), so you may not like the look of the resulting expression. >> E.g., you might find floating point approximations to certain numbers >> instead of a "perfectly precise" answer.

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[math-fun] Scientific American: Fleischmann-Pons reconsidered
by Bill Gosper 19 Dec '16

19 Dec '16

On 2016-12-18 11:38, Henry Baker wrote: > FYI -- The only reason for posting this is that it comes from a high > quality source. SciAm? > > "There are more things in heaven and earth, Horatio, then are dreamt than > of in your philosophy" -- Shakespeare. According to Mathematica, In[468]:= WordDefinition["undreamt"] Out[468]= {"not imagined even in a dream"} is a word, but In[469]:= WordDefinition["dreamt"] (Dialog) Out[469]= Missing["NotAvailable"] isn't. Shakespearean English is fading away. --rwg > > https://blogs.scientificamerican.com/guest-blog/its-not-cold-fusion-but- its-something/ > > It's Not Cold Fusion... But It's Something > > An experiment that earned Stanley Pons and Martin Fleischmann > widespread ridicule in 1989 wasn't necessarily bogus > > By Steven B. Krivit, Michael J. Ravnitzky on December 7, 2016 > > ... > > Data show that changes to atomic nuclei, including observed *** shifts > in the abundance of isotopes, can occur without high-energy > accelerators or nuclear reactors. *** For a century, this has been > considered impossible. In hindsight, glimpses of the new phenomena > were visible 27 years ago. > > ... > > The Widom-Larsen theory has nothing to do with fusion; the key steps > are based on weak interactions and are consistent with existing > physics. The theory explains how nuclear reactions can occur at or > near room temperature through the creation of ultra-low-momentum > neutrons and subsequent neutron-capture processes. Such neutrons, > according to the theory, have a very large DeBroglie wavelength and > therefore have a huge capture cross section, explaining why so few > neutrons are detected. > > ... > > Reports also show that LENRs [low energy nuclear reactions] can > produce local surface temperatures of 4,000-5,000K and boil metals > (palladium, nickel and tungsten) in small numbers of scattered > microscopic sites on the surfaces of laboratory devices. > > ... > > For nearly three decades, researchers in the field have not observed > the emission of dangerous radiation. Heavy shielding has not been > necessary. > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Protect your address bits!
by Thane Plambeck 19 Dec '16

19 Dec '16

http://billypenn.com/2016/12/13/binary-bandits-heart-grows-3-sizes-83-1s-0s… -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] Scientific American: Fleischmann-Pons reconsidered
by Henry Baker 18 Dec '16

18 Dec '16

FYI -- The only reason for posting this is that it comes from a high quality source. "There are more things in heaven and earth, Horatio, then are dreamt of in your philosophy" -- Shakespeare. https://blogs.scientificamerican.com/guest-blog/its-not-cold-fusion-but-its… It's Not Cold Fusion... But It's Something An experiment that earned Stanley Pons and Martin Fleischmann widespread ridicule in 1989 wasn't necessarily bogus By Steven B. Krivit, Michael J. Ravnitzky on December 7, 2016 ... Data show that changes to atomic nuclei, including observed *** shifts in the abundance of isotopes, can occur without high-energy accelerators or nuclear reactors. *** For a century, this has been considered impossible. In hindsight, glimpses of the new phenomena were visible 27 years ago. ... The Widom-Larsen theory has nothing to do with fusion; the key steps are based on weak interactions and are consistent with existing physics. The theory explains how nuclear reactions can occur at or near room temperature through the creation of ultra-low-momentum neutrons and subsequent neutron-capture processes. Such neutrons, according to the theory, have a very large DeBroglie wavelength and therefore have a huge capture cross section, explaining why so few neutrons are detected. ... Reports also show that LENRs [low energy nuclear reactions] can produce local surface temperatures of 4,000-5,000K and boil metals (palladium, nickel and tungsten) in small numbers of scattered microscopic sites on the surfaces of laboratory devices. ... For nearly three decades, researchers in the field have not observed the emission of dangerous radiation. Heavy shielding has not been necessary.

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[math-fun] The difficulty of integration vs. the ease of differentiation
by Bill Gosper 17 Dec '16

17 Dec '16

Julian, as usual, sent this only to me. I don't know how to make the question rigorous, but I think one answer is that differentiation is a local operation, and integration isn't. This contributes significantly to the practical fact of the chain rule, which is what usually makes differentiation easy (often via product, inverse, etc. which are easily derived from it). The "chain rule" for integration would be change-of-variables, which has ickiness both in how it changes the domain and the Jacobian involving inverse functions. (You need to consider multivariable because that's where the product rule comes from.) Julian (per rwg) Date: 2016-12-16 13:54 From: Dan Asimov <asimov(a)msri.org> Why is it usually so easy to differentiate a function defined by an exact formula, but so much more difficult to integrate? If this question can be made rigorous, how might that be done? (And if so, what is the rigorous answer, or at least a method of approaching it?) —Dan

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[math-fun] The difficulty of integration vs. the ease of differentiation
by Bill Gosper 16 Dec '16

16 Dec '16

Date: 2016-12-16 14:08 From: James Propp <jamespropp(a)gmail.com> Relatedly: Why is it so easy to obtain a formula for f(n)-f(n-1) given a formula for f(n), but so hard to obtain a formula for f(1)+f(2)+...+f(n) given a formula for f(n)? :-) Jim Propp https://www.ncbi.nlm.nih.gov/pmc/articles/PMC411178/pdf/pnas00013-0045.pdf :-) On Friday, December 16, 2016, Dan Asimov <asimov(a)msri.org> wrote: > Why is it usually so easy to differentiate a function defined by an > exact formula, but so much more difficult to integrate? > > If this question can be made rigorous, how might that be done? > > (And if so, what is the rigorous answer, or at least a method of > approaching it?) > > —Dan A sort of counterexample is that if you can differentiate d/ds HurwitzZeta(s,a), you can do fancy integrals of t^s log t! . http://gosper.org/filds.pdf pp 1, 5. And sure enough, that derived function is hard to compute. --rwg

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[math-fun] Morley.gif
by Bill Gosper 15 Dec '16

15 Dec '16

I just giffed Julian's old San Jose Math Circle animation of Morley's verified conjecture: The trisectors of the vertex angles of a triangle always make an *equilateral* triangle. gosper.org/Morley.gif . (Firefox probably has the best gif player.) --rwg

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[math-fun] Draft of my December 2016 blog post
by James Propp 14 Dec '16

14 Dec '16

I started writing a new draft titled "Why '17 will be the Year of the Pig" and would love to get your feedback. I plan on publishing it on the 17th. Suggestions of all kinds are welcome. Please leave your feedback here: https://mathenchant.wordpress.com?p=1372&shareadraft=58504bdb7e2be keeping in mind that the comments of EVERYONE on math-fun will get funneled through the same email conduit; if you want me to know who you are, please sign your comments! If you sign your comments I'll assume (unless you indicate otherwise) that you don't mind my acknowledging your contribution. Title: Why '17 will be the Year of the Pig Beginning: You probably haven't heard of David C. Kelly; he doesn't give TED talks, or probe the human genome, or push back the frontiers of particle physics and cosmology, or uncover the unexpected social consequences of algorithm design. But he's inspired and nurtured hundreds of people who've done these thi... Read more: https://mathenchant.wordpress.com?p=1372&shareadraft= 58504bdb7e2be Thanks, Jim Propp

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