August 2012 - mathfun@mailman.xmission.com

[math-fun] helical slide rule
by Warren Smith 31 Aug '12

31 Aug '12

It seems to me (fulfilling my role as Great Improver of obsolete past technologies) that the most compact way to make a high precision slide rule would be helical. Circular? Linear? Garbage.

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Re: [math-fun] helical slide rule
by Henry Baker 31 Aug '12

31 Aug '12

I'm wondering if there's anything in the plant or animal kingdom that utilizes something like a nomogram/nomograph for estimating some function. --- On a related note, I heard a virologist say that there's a virus that is so highly developed, that it reads DNA groups of 3 _starting at EVERY location_, both BACKWARDS and FORWARDS. (Most DNA can be read in groups of 3 only at mod(3) boundaries, and can only read forwards.) If so, eat your heart out, Bach! You've been outdone by a lowly virus! Perhaps someone can convert this virus's DNA into polyphonic music? At 08:22 PM 8/30/2012, Warren Smith wrote: >It seems to me (fulfilling my role as Great Improver of obsolete past technologies) >that the most compact way to make a high precision slide rule would be helical. >Circular? Linear? Garbage.

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Re: [math-fun] zooming in on the reals
by Bill Gosper 31 Aug '12

31 Aug '12

Mike Stay> On Wed, Aug 29, 2012 at 6:24 AM, James Propp <jamespropp(a)gmail.com <http://gosper.org/webmail/src/compose.php?send_to=jamespropp%40gmail.com>> wrote:> Has anyone created interactive software that lets one zoom in on the real line? I'm imagining a line on the screen that doesn't change at all as you zoom in. -- Mike Stay - metaweta(a)gmail.com <http://gosper.org/webmail/src/compose.php?send_to=metaweta%40gmail.com>http://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com No, no, that's much too thick! You shouldn't be able to see it. Apropos nonelectronic calculation, if you have a youngster, hardcopy it this extended times table <http://gosper.org/kellytable.png>. Filling this in should cement intuitions about minus times minus, even times odd, primes, and progressions, e.g. --rwg Apologies for many links breaking on gosper.org . We're looking into it. I'll fix the ones people tell me.

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[math-fun] postscript slide rules and nomograms
by Robert Munafo 30 Aug '12

30 Aug '12

On 8/30/12, Mike Speciner <ms(a)alum.mit.edu> wrote: > [...] It's > amazing how clever nomographers could be, but of course now that just > about everyone carries around an electronic computation device, it is a > lost art. It did, however, inspire me some years later to write a pile > of PostScript to (amongst other things) plot nomograms: > https://dl.dropbox.com/u/17718830/plot.ps > I suppose writing PostScript has also become a lost art. I created a nomogram for x^(x^(y-1))=z, which is the lower hyper4 operator (http://mrob.com/pub/math/hyper4.html#lower4) and here is a sliderule that calculates x^y=z and its inverses in the range e^0.001 <= z <= e^100 ~ 10^43: http://mrob.com/pub/math/sliderules.html#model3 Co-workers noted the immense amount of computer power that has gone into creating this low-precision analogue device. I certainly still remember PostScript programming, and there is much more to nomography (than I ever learned). -- 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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Re: [math-fun] zooming in on the reals
by Dave Dyer 30 Aug '12

30 Aug '12

At 09:42 AM 8/30/2012, James Propp wrote: >That would certainly be easy to code. We don't know the identities of very many interesting numbers. I suppose it would be easy and moderately interesting to zoom in on the zone containing pi e e^pi pi^e and so on. Expanding the space between each pair of rationals to include infinitely many more rationals would be fairly straightforward but boring; but how would you represent the infinite number of irrationals between each of the infinitely many rationals you can't even see yet?

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Re: [math-fun] zooming in on the reals
by Phil Carmody 30 Aug '12

30 Aug '12

From: Dan Asimov <dasimov(a)earthlink.net> > What features do you want to display? (And > how could you omit this from your question?!?) > > On 2012-08-29, at 6:24 AM, James Propp wrote: > << Has anyone created interactive software that lets one zoom in on the real line? Half of the problem when answering a question is to work out what the question should be! Were I to have make the request, I think I'd relate the zoom depth to Kolmogorov complexity given some fairly simple alphabet of terminal symbols, for example what we're happy us mostly unambiguous when using in ASCII text. If a real has a short enough expression to generate it, plot it on the line. I'd leave "relate" and "short enough" as an exercise for the implementor! ;-) Phil

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Re: [math-fun] elliptic curve calculator
by Phil Carmody 30 Aug '12

30 Aug '12

From: "Adam P. Goucher" > > > http://cp4space.wordpress.com/2012/08/29/elliptic-curve-calculator/ > > Warren wrote: > > "Why is this better than a slide rule?" > > It can compute square roots, If you're printing out your slide rule, square root calculation is just folding the slide rule in 2, or other disection. > is much cheaper, Not if you're also printing your slide rule out on paper. (My first slide rule was hand-made from paper stuck to card, made after seeing my dad's old school slide rule from the days before anything electronic.) > and doesn't require any moving parts. Not so, there's the straight edge that you have to manipulate. > It's more of a demonstration of the interchangeability of elliptic curves > and modular arithmetic, not a suggestion that this be used for practical > purposes. And indeed for that it was most interesting, as I too had not encountered Guy's original formulation before. Phil

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[math-fun] Elliptic curve calculator
by Adam P. Goucher 30 Aug '12

30 Aug '12

You may be aware of the Abelian group operation on elliptic curves. We can exploit this to multiply, divide and square-root real numbers just by drawing a straight line on an elliptic curve marked with two logarithmic scales: http://cp4space.wordpress.com/2012/08/29/elliptic-curve-calculator/ I've tried it on a printed version, and can achieve somewhere between 2 and 3 significant figures of precision, depending on the calculation. Obviously it is of no practical use today, since we have electronic calculators and so forth. But in theory, this could have been made way back in 1830, when it could have been used for calculations in navigation and ballistics. Sincerely, Adam P. Goucher http://cp4space.wordpress.com/

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[math-fun] Slide rule versus alleged 2D improvements
by Warren Smith 30 Aug '12

30 Aug '12

I've got a slide rule somewhere which does square roots. Multiply, divide, log, exp, squareroots, add, subtract. Plus I can draw a sliderule myself with litte or no aid. To draw that elliptic curve thingummy, I'd probably need a computer. --- So it seems to me, if you want to go beyond the sliderule, then you need to compute a function of THREE arguments. Suppose there were a curve on a 2D plane, labeled with numeric scales. Also in the plane is a 2D grid, labeled ditto. And you had a straightedge with a numeric scale on it and sliding T-square. You could intersect the straightedge with two given points on the curve, plus slide the T-square to intersect a third given point on the curve. Finally the point where the Tsquare and straightedge intersected, could be read off the grid. Hence you would be computing a function of three arguments. There might be other and better ways to do it. Question is, can we make something like this useful?

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[math-fun] Diane Rehm: Is Algebra Necessary?
by Henry Baker 29 Aug '12

29 Aug '12

FYI -- WAMU-FM: WAMU: The Diane Rehm Show Podcast >From NPR and WAMU 88.5 FM in Washington, DC, The Diane Rehm Show is a live, award-winning NPR program featuring smart conversation and civil dialogue on top news stories and new ideas, two hours a day, five days a week. Is Algebra Necessary? Wednesday, August 29, 2012 10:15 AM Algebra has long been a required math course for teenagers, but some argue it's not for all students. Differing views on the value of teaching algebra. Media files WAMU_160253207.mp3 (VLC media file (.mp3), 23.6 MB) 52 minutes long. http://podcastdownload.npr.org/anon.npr-podcasts/podcast/305/510071/1602532…

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