December 2014 - mathfun@mailman.xmission.com

[math-fun] calculus books for English majors?
by Warren D Smith 13 Dec '14

13 Dec '14

I don't see what is the matter with just a pretty normal calculus textbook. Some of them are quite decent nowadays. And I do not believe in math books "for the layperson" or "for dummies" etc. Get math books intended for people who really want to learn/use the math.

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[math-fun] bizarre response from http://isc.carma.newcastle.edu.au/standardCalc
by Bill Gosper 13 Dec '14

13 Dec '14

I unwittingly gave it .39269908169872415480783042290994 == N[π/8, 32] and got three answers: Best guess: sol of (1-tan(x))/log(x) sol of (1-tan(x))/log(x) 3926990816987241 sol of cos(x)/(W(x)+exp(x)) sum(1/(16*n^2-16*n+3),n=1..inf) <http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html> I just realized that the first two are satisfied by 10π/8. And would remain so without those exotic denominators. Looks like they need to hire Rob Munafo. --rwg

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[math-fun] more mystery constants
by Bill Gosper 12 Dec '14

12 Dec '14

Who first noticed Somos4 sequences satisfied theta fcn recurrences--Elkies? See, e.g., the "period 8" 0,1,1,-1,-2/3,1/3,1/9,-1/27,0,... near the top of p13 of http://arxiv.org/abs/math/0703470 . I still don't understand why we never need a geometric scale factor (e.g. c^n). At any rate, ISC doesn't recognize any of the four buggerfactors b, u, y, and Q. No problem, just use Jacobi's imaginary transformation, and we get, oops, four new unrecognizables. --rwg

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[math-fun] area inside algebraic curve impossible to express?
by Warren D Smith 12 Dec '14

12 Dec '14

> From: Victor Miller <victorsmiller(a)gmail.com> > I would expect that the area of the region is given by an elliptic > integral. Use Green's theorem to show that the area is > integral y dx where the integral is over the path of the bounding curve. > The bounding curve is binational to an elliptic curve, and so is > parametrized by elliptic functions. > --uh... really? I thought that general cubic curves are NOT birational to elliptic curves. But no: http://en.wikipedia.org/wiki/Algebraic_curve#Elliptic_curves says they are. Oh. That suggests to get an area that is not expressible in closed form (if elliptic functions are allowed in the closed form) we need an algebraic curve of degree 4. These are in general NOT birational to elliptic curves since they generally have genus 3, while elliptics have genus 1. It is true that y^2 = quartic(x) if has a rational point is birationally elliptic, but these are not general curves. Anyhow, back in my original conjecture, I presume no closed form is possible if we do not allow elliptics in the formulas. I further presume that general elliptic functions evaluated at rational arguments in general yield numbers not expressible in lower-tech ways,

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[math-fun] area inside algebraic curve impossible to express?
by Warren D Smith 12 Dec '14

12 Dec '14

For an explicit impossibility conjecture, consider the finite-area loop containing (-2,1) bounded by the fairly-generic-looking cubic curve 3x^3 + 4x^2y + 7y^2x - 10y^3 - 36x + 37y = 41. I doubt this area, which is approximately 4.68450311946587, can be expressed in closed form. [Number found using polar coordinates centered at (-2.2, 1.1); integrate (r^2/2) dtheta using trapezoidal rule. All digits probably correct.] If anybody recomputed this to, say, 50 decimals, then huge runs of number-guesser tools could partially confirm the conjecture, I guess. Ries -l6 realizes it has nothing & gives up in disgust. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Peer2peer-reviewed papers
by Hilarie Orman 10 Dec '14

10 Dec '14

If nothing else, that log formula is a giveaway of dissociated press (dp++ = SCIgen). Hilarie > Date: Wed, 10 Dec 2014 15:12:30 -0800 > From: Henry Baker <hbaker1(a)pipeline.com> > Subject: [math-fun] Peer2peer-reviewed papers > FYI -- Maggie Simpson takes time out from her busy TV schedule to write a scientific paper. > Perhaps she should have chosen Ibm Watson as a co-author? > Some of the references are pretty amusing. > http://aperito.org/uploads/pdf/AJN-1-101.pdf > Aperito Journal of Nanoscience Technology > Received: Sep 16, 2014 > Accepted: Oct 10, 2014 > Published: Oct 14, 2014 > Fuzzy, Homogeneous Configurations > Margaret Simpson, Kim Jong Fun and Edna Krabappel > Department of Electrical and Computer Engineering, Belford University, USA > Abstract > The Ethernet must work. In this paper, we confirm the > improvement of e-commerce. WEKAU, our new > methodology for forward-error correction, is the solution > to all of these challenges. > Introduction > Unified perfect symmetries have led to many unproven > advances, including Markov models and write-ahead logging. > While prior solutions to this quagmire are excellent, none have > taken the real-time method we propose in this work. On a > similar note, this is a direct result of the evaluation of > replication. Obviously, Internet QoS and reliable information > are rarely at odds with the deployment of journaling file > systems. > We disprove that the Internet [1], [1] and the UNIVAC > computer can agree to address this issue. Indeed, Lamport > clocks and 802.11 mesh networks have a long history of > connecting in this manner. The usual methods for the study of > spreadsheets do not apply in this area. Along these same lines, > the shortcoming of this type of solution, however, is that > massive multiplayer online role-playing games [2], [3] and > lambda calculus can cooperate to solve this quandary. ... > Our design avoids this > overhead. Davis et al. [13] developed a similar heuristic, on the > other hand we disproved that WEKAU runs in O (log log log > log N !) time [10, 8, 14-18]. Although this work was published > before ours, we came up with the approach first but could not > publish it until now due to red tape (Figure 1). > B. Experiments and Results > Is it possible to justify the great pains we took in our > implementation? No. > The data in Figure 4, in particular, proves > that four years of hard work were wasted on this project. The > results come from only 9 trial runs, and were not reproducible. > Lastly, we discuss the second half of our experiments. Error > bars have been elided, since most of our data points fell outside > of 78 standard deviations from observed means. Note the heavy > tail on the CDF in Figure 3, exhibiting improved median > distance [6]. Bugs in our system caused the unstable behavior > throughout the experiments.

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[math-fun] Peer2peer-reviewed papers
by Henry Baker 10 Dec '14

10 Dec '14

FYI -- Maggie Simpson takes time out from her busy TV schedule to write a scientific paper. Perhaps she should have chosen Ibm Watson as a co-author? Some of the references are pretty amusing. http://aperito.org/uploads/pdf/AJN-1-101.pdf Aperito Journal of Nanoscience Technology Received: Sep 16, 2014 Accepted: Oct 10, 2014 Published: Oct 14, 2014 Fuzzy, Homogeneous Configurations Margaret Simpson, Kim Jong Fun and Edna Krabappel Department of Electrical and Computer Engineering, Belford University, USA Abstract The Ethernet must work. In this paper, we confirm the improvement of e-commerce. WEKAU, our new methodology for forward-error correction, is the solution to all of these challenges. Introduction Unified perfect symmetries have led to many unproven advances, including Markov models and write-ahead logging. While prior solutions to this quagmire are excellent, none have taken the real-time method we propose in this work. On a similar note, this is a direct result of the evaluation of replication. Obviously, Internet QoS and reliable information are rarely at odds with the deployment of journaling file systems. We disprove that the Internet [1], [1] and the UNIVAC computer can agree to address this issue. Indeed, Lamport clocks and 802.11 mesh networks have a long history of connecting in this manner. The usual methods for the study of spreadsheets do not apply in this area. Along these same lines, the shortcoming of this type of solution, however, is that massive multiplayer online role-playing games [2], [3] and lambda calculus can cooperate to solve this quandary. ... Our design avoids this overhead. Davis et al. [13] developed a similar heuristic, on the other hand we disproved that WEKAU runs in O (log log log log N !) time [10, 8, 14-18]. Although this work was published before ours, we came up with the approach first but could not publish it until now due to red tape (Figure 1). B. Experiments and Results Is it possible to justify the great pains we took in our implementation? No. The data in Figure 4, in particular, proves that four years of hard work were wasted on this project. The results come from only 9 trial runs, and were not reproducible. Lastly, we discuss the second half of our experiments. Error bars have been elided, since most of our data points fell outside of 78 standard deviations from observed means. Note the heavy tail on the CDF in Figure 3, exhibiting improved median distance [6]. Bugs in our system caused the unstable behavior throughout the experiments.

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[math-fun] I misunderstood Apple's special characters menu
by Bill Gosper 10 Dec '14

10 Dec '14

to propose ten different Chinese characters for ⅘: 姘姣娣娴婵嫉嫌嫜嫡馗 But Google translate gives Mistress Pretty Di Xian Chan Jealous Suspicion Husband's parent First wife Cheekbone Does Chinese have a ⅘ character? --rwg Husband's parent. Wow.

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Re: [math-fun] $19.99 and all that
by Henry Baker 10 Dec '14

10 Dec '14

Low-order digits in pricing have also been used for signalling in auction bidding and in price-fixing among vendors. I wonder how these "Turing-type" effects are handled by classical economic theory? At 12:22 AM 12/10/2014, Seb Perez-D wrote: >Major retailers use the final digits of the price to signal which items are >"marked down, specially priced, rebate items, discontinued, or will be not >be restocked". > >I'd bet this is not for psychological reasons, but one never knows. > >http://lifehacker.com/know-the-secret-price-codes-at-major-retailers-to-sav… > >http://lifehacker.com/save-even-more-money-at-costco-by-knowing-their-secre…

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[math-fun] $19.99 and all that
by James Propp 10 Dec '14

10 Dec '14

We all know that subjective price is a nonlinear function of monetary price (that's just a fancy way of saying that $19.99 "feels" like significantly less money than $20). But is it possible that subjective price is (for some people, under some circumstances) a non-monotone function of monetary price? That is, might $7.01 "feel" like more money than $8 (for instance)? I'd be curious to know if this has ever been studied. For that matter, is there experimental evidence backing up the idea that you can make people significantly more willing to buy a $20 consumer product by knocking a penny off the price? I should mention that I'm aware that there have been instances in which raising the price of an item increased the demand for the item (because the higher price marked it as a luxury item, and then people wanted to buy the prestige that came along with the higher pricetag). But that's not quite what I'm asking about. Jim Propp

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