January 2013 - mathfun@mailman.xmission.com

[math-fun] Repeating decimal expansion
by Eric Angelini 02 Feb '13

02 Feb '13

Hello Math-Fun, à propos the table "Repeating decimal expansion", here: http://thestarman.pcministry.com/math/rec/RepeatDec.htm ... I read that: 1/2 = 0.5 1/4 = 0.25 1/5 = 0.2 ... but is this equivalent to: 1/2 = 0.499999999999999999999999999999... 1/4 = 0.249999999999999999999999999999... 1/5 = 0.199999999999999999999999999999... And what about: 1/3 = 0.6666666666666666666666666666666... ... re-written as: 1/3 = 0.6599999999999999999999999999999... 1/3 = 0.6666659999999999999999999999999... 1/3 = 0.6666666666666666666666599999999... I'm confused. Best, É.

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[math-fun] important contribution to Indian mathematics
by Bill Gosper 01 Feb '13

01 Feb '13

The equation of the samosa! ParametricPlot3D[{Cos[t], Cos[u], Cos[u + t]}, {t, 0, 2 π}, {u, 0, π}] (Rounded regular tetrahedron, four vertices, no edges, but contains the line segments joining the vertices.) Implicit equation: acos(z)=acos(x)+acos(y) Volume pi^2/2 Area (empirical) 5 pi, but I can't get Mma to do the integral. This can't be new. Does this surface have a legitimate name? Can anyone prove the area? --rwg

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[math-fun] TJX markup/text formatter?
by quad 31 Jan '13

31 Jan '13

Hello math-fun, I guess Abelson sent a friend of mine a paper in TJX format. Or maybe the text formatter was called TJX? Does anyone know what this is? Any interesting history? Apparently it's an archaic format(ter) before my time. I can't find anything on Google about it. Thanks, Robert Smith

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Re: [math-fun] Curious function
by Robert Munafo 31 Jan '13

31 Jan '13

Hey thanks Fred! Your mind-reader machine managed to figure out how the word "asymptotic" applies to Dan's riddle. All I got was a recurrence relation, which of course is not closed-form. But I was stumped by "asymptotic". But since these are Lucas numbers, then course, there must be an *exact*, closed form formula too (just as with the Fibonacci numbers) viz.: ((3-sqrt(5))^n + (3+sqrt(5))^n)/2^n This formula was contributed to A005248 by Creighton Dement back in Apr 19 2005. Remember "Floretions"? So we have a closed-form, exact not asymptotic, answer. On 1/31/13, Fred W. Helenius <fredh(a)ix.netcom.com> wrote: > [...] > > 2, 3, 7, 18, 47, 123, 322, 843, 2207, 5778, 15127, ... > > This is the subsequence of the Lucas sequence consisting of > the terms with even index. Since L(n) = phi^n + (-1/phi)^n, > f(n) = L(2n) is asymptotic to phi^{2n}, where phi is the > golden ratio. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com

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[math-fun] Mathematicians aim to take publishers out of publishing
by Henry Baker 30 Jan '13

30 Jan '13

FYI -- http://www.nature.com/news/mathematicians-aim-to-take-publishers-out-of-pub… Mathematicians aim to take publishers out of publishing Episciences Project to launch series of community-run, open-access journals. Richard Van Noorden 17 January 2013 Corrected: 17 January 2013 Jean-Pierre Demailly is a leader in an effort to create a researcher-run publishing system. Mathematicians plan to launch a series of free open-access journals that will host their peer-reviewed articles on the preprint server arXiv. The project was publicly revealed yesterday in a blog post by Tim Gowers, a Fields Medal winner and mathematician at the University of Cambridge, UK. The initiative, called the Episciences Project, hopes to show that researchers can organize the peer review and publication of their work at minimal cost, without involving commercial publishers. ÂItÂs a global vision of how the research community should work: we want to offer an alternative to traditional mathematics journals,Â says Jean-Pierre Demailly, a mathematician at the University of Grenoble, France, who is a leader in the effort. Backed by funding from the French government, the initiative may launch as early as April, he says. Many mathematicians Â and researchers in other fields Â claim that they already do most of the work involved in publishing their research. At no cost, they type up and format their own papers, post them to online servers, join journal editorial boards and review the work of their peers. By creating journals that publish links to peer-reviewed work on servers such as arXiv, Demailly says, the community could run its own publishing system. The extra expense involved would be the cost of maintaining websites and computer equipment, he says. That cost is not small, but it could eventually be provided in part by the journals' users. The arXiv server, for example, costs about US$826,000 a year to run, and is funded by the Cornell University Library in Ithaca, New York; the Simons Foundation in New York and institutional members. Demailly says that he first thought of open-access electronic journals that overlay arXiv eight years ago, but the concept became a reality only last June, when he was contacted by the Centre for Direct Scientific Communication (CCSD), based in Villeurbanne, France. The CCSD, a unit of the French National Centre for Scientific Research, develops open-access repositories such as the multidisciplinary archive HAL, which mirrors the arXiv site. For the Episciences Project, the CCSD plans to create a publishing platform that will support online peer-reviewed journals. Each journal, or ÂepijournalÂ, would have its own editor and editorial board, and authors could submit their arXiv-posted papers to their journal of choice. The journal would then organize peer review, perhaps using workflow software provided by the CCSD. Peer-reviewed papers would be posted on arXiv alongside their un-reviewed versions. A central committee (led by Demailly) would manage new journal candidates and make recommendations on paper formatting, but each journal would be free to set its own policies (including whether to charge for publication). Gowers plans to start a journal in the interdisciplinary field of additive combinatorics; Demailly would not say what other early epijournals might be. Gowers has strong views on shaking up research publishing Â last year, he kick-started a boycott of the Dutch publishing giant Elsevier (see also NatureÂs profile of Gowers). The idea of overlaying arXiv is not new: some mathematics journals tried it in the early 2000s but scrapped the idea because libraries began dropping print subscriptions, says Demailly. Meanwhile, there are already some free, community-organized mathematics journals, such as Documenta Mathematica, funded by the German Mathematical Society. ÂThey are doing things on their own with a small website; we will have a global platform capable of drastically reducing an individual journalÂs administration costs,Â Demailly says. Demailly says that he expects to adjust the concept with feedback from the mathematics community. ÂIf people want larger reviews linked to papers, or the possibility of online comments and blogs, we can offer this with only minor changes to the platform,Â he says. At the moment, the model's success or failure hinges on buy-in from mathematicians Â but the involvement of Gowers and other prominent mathematicians, such as Terence Tao of the University of California, Los Angeles, may help to build support. Nature doi:10.1038/nature.2013.12243 Corrections Corrected: An earlier version of this story misstated the annual cost of the arXiv as $200,000 instead of $826,000. This has now been corrected.

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Re: [math-fun] Repeating decimal expansion
by Adam P. Goucher 29 Jan '13

29 Jan '13

> > I hope this simple solution will stop the silly discussions about 0 being > > a natural number. My hope will be in vain, I know. That's why it's better to use $\mathbb{Z}_{\geq 0}$ or $\mathbb{Z}_{\geq 1}$ instead of the ambiguous $\mathbb{N}$. Sincerely, Adam P. Goucher

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Re: [math-fun] New way to visualise complex functions
by Adam P. Goucher 29 Jan '13

29 Jan '13

> Nice! You might also try, instead of a world map, using a human face as the > base image, making expressions of expressions, so to speak. Good idea! I know someone called Ross Atkins, who has half a beard for the sole purpose of determining whether an image of his face has been reflected. This, of course, is also applicable to affine transformations and the conformal/anticonformal maps explored on the cp4space post. Sincerely, Adam P. Goucher

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[math-fun] New way to visualise complex functions
by Adam P. Goucher 28 Jan '13

28 Jan '13

Tim Large suggested an idea of how to visualise functions from the complex plane to the extended complex plane. Some preliminary results are shown on the webpage below: http://cp4space.wordpress.com/2013/01/27/visualising-complex-functions/ I should be able to make this into a Wolfram Demonstration. Sincerely, Adam P. Goucher

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Re: [math-fun] Geometry puzzle -- spoiler
by Adam P. Goucher 26 Jan '13

26 Jan '13

It's possible entirely with the 'power of a point' paradigm: Let the line segment RSP intersect C again at T. By the tangent- secant theorem, RQ^2 = RS.RT, so RT = 12^2/8 = 18. Hence, ST = 10 and PT = 6. The power of P with respect to C is -(PS.PT) = -24, which is also the value of OP^2 - r^2. Since OP^2 = 16, we can deduce that r^2 = 40 and thus r = sqrt(40). Sincerely, Adam P. Goucher http://cp4space.wordpress.com > ----- Original Message ----- > From: davidwwilson(a)comcast.net > Sent: 01/26/13 06:32 PM > To: math-fun > Subject: Re: [math-fun] Geometry puzzle > > Sorry, let's try again > > > Let segment PR cut C at point S bete > > > This was a problem posed to me by a friend: > > Let circle C have center O. > > Let point P satisfy OP = 4. > > Draw tangent line L to C at point Q. Place point R on L with QR = 12. > > Let segment PR cut C at point S so that RS = 8 and RP = 12. > > What is the radius of C? > > > Perhaps I got it right this time. > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Divisors of divisors
by Charles Greathouse 26 Jan '13

26 Jan '13

Given a multiset S, how can we determine whether there is an integer n such that each s in S corresponds to (is in bijection with) a divisor t of n such that d(t) = s? This came up recently when considering multisets with the property s_1^3 + s_2^3 + ... + s_k^3 = (s_1 + s_2 + s_3 + ... + s_k)^2. One infinite family are the multisets with this divisor-of-divisors property. Another is {n, n, ..., n} with n elements. Charles Greathouse Analyst/Programmer Case Western Reserve University

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