February 2010 - mathfun@mailman.xmission.com

Re: [math-fun] What is the correct word for . . .
by Dan Asimov 15 Feb '10

15 Feb '10

I think they do deserve to have their own name if they don't already. ((( (Could the word "surd" have precisely this meaning, or does that word either have only a vague definition, or a more limited precise definition?) Otherwise, some word with a sense similar to "constructible" would be a good candidate. And < thesaurus.com > has no listing for "constructible". ))) I think Marc's suggestion of "solvable" numbers is an excellent one. I don't think this term is taken, and "solvable numbers" is nicely consistent with Bill's comment that these numbers are precisely those having a solvable Galois group. If no one objects, then by the powers invested in me by the Math Goddess I hereby declare "solvable" the official name of such numbers. --Dan Bill Thurston wrote: << These are, in other words, algebraic numbers with solvable Galois group, which may be a reasonable way to specify them. Do they deserve to have a 1-word name? It would be tempting to call them "radical numbers" except that they're not actually so radical, they're comparatively tame among algebraic numbers. "Constructible numbers" is already taken, by the special case of algebraic numbers whose Galois group is a 2-group. Bill On Feb 15, 2010, at 2:41 PM, Dan Asimov wrote: > . . . real numbers that can be expressed using > integers, addition, subtraction, multiplication, division, > and integer roots and powers -- starting with integers > or rationals? > > How about all such (real or) complex numbers? > > (As distinguished from the rest of the algebraic numbers.) >> ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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Re: [math-fun] What is the correct word for . . .
by Henry Baker 15 Feb '10

15 Feb '10

This may be what you want: "real closed fields" encompass all of the solutions of polynomials with integer coefficients & is closed under addition, subtraction, multiplication & division & roots & powers (so long as the roots & powers have fixed constant integer roots & powers). [I believe that the second half of the previous sentence is redundant.] Clearly the elements of real closed fields are a countable set. At 11:41 AM 2/15/2010, Dan Asimov wrote: >. . . real numbers that can be expressed using >integers, addition, subtraction, multiplication, division, >and integer roots and powers -- starting with integers >or rationals? > >How about all such (real or) complex numbers? > >(As distinguished from the rest of the algebraic numbers.) > >--Dan

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[math-fun] What is the correct word for . . .
by Dan Asimov 15 Feb '10

15 Feb '10

. . . real numbers that can be expressed using integers, addition, subtraction, multiplication, division, and integer roots and powers -- starting with integers or rationals? How about all such (real or) complex numbers? (As distinguished from the rest of the algebraic numbers.) --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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Re: [math-fun] Symbol for rotation?
by Bill Gosper 15 Feb '10

15 Feb '10

> (Also, though I hate to floccinaucinihilipilificate, I cannot find any trace > of a neolasiopteran clade. The Lasiopteridi show no signs of one. Have you > been creating bionic gall midges in your secret laboratory?) That would explain those damned gnats in my bedroom. Especially the galling part. Would you like to bet against the emergence of such a clade? There's actually a whole network of these laboratories cranking out mutations and smuggling them into undeveloped countries so that our armies of surplus entomologists (soon to be thronged by ex-climatologists) can remain employed by weekly announcing new species. Things are so tough that a certain Dr. Cascara Buckthorn moonlights as a thrip teaser. --rwg Dr.'s kid Mondegreen: I grew up thinking they were tungdy pressers.

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Re: [math-fun] Symbol for rotation?
by Dan Asimov 14 Feb '10

14 Feb '10

And I thought statune meant keep listening to this radio station. << That's better than me. I thought it was the donzerly light. ----- Original Message ----- From: "Bill Gosper" <billgosper(a)gmail.com> To: <math-fun(a)mailman.xmission.com> Sent: Saturday, February 13, 2010 11:14 PM Subject: Re: [math-fun] Symbol for rotation? > Dr.'s kid Mondegreen: I grew up thinking they were tungdy pressers. >> ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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[math-fun] Mathematical and Scientific Joke Competition
by Ray Tayek 13 Feb '10

13 Feb '10

http://www.simonsingh.com/Joke_Competition.html " ... I received dozens of entries for the world's funniest mathematical or scientific joke. I published my favourite fifteen and asked for your votes. Below you will find the winning joke sent in by Robert Williams and the fourteen runners-up. ... " --- co-chair http://ocjug.org/

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Re: [math-fun] Symbol for rotation?
by Dan Asimov 13 Feb '10

13 Feb '10

RWG writes: << I don't like the circled dot. Isn't it already astro***ical for Sun? How about a circular little arrow. Then we'd have a cw and ccw sign option, and maybe even fractional turn and phase variations via lightface or dotted segments. >> Makes sense. But the likelihood of a symbol's being used is inversely proportional to the amount of writing it requires.* So maybe letting that circular arrow evolve naturally, it would become something like an upper semicircle with a short vertical stroke on its left or on its right . . .? Alternatively, a sideways 6 vs. a sideways 9 might work. * * * As for *why* anyone would want such a symbol: In some research I'm doing, for a long time I've been writing fractions of a circle in radians and finally got tired of writing all those pis when only which fraction of a circle -- not its arclength -- is relevant. --Dan ____________________________________________________________________ * This is the *real* reason that more numbers start with 1 than with other digits, pace Benford's Law. ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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Re: [math-fun] Symbol for rotation?
by Bill Gosper 12 Feb '10

12 Feb '10

On Thu, Feb 11, 2010 at 2:52 PM, Dan Asimov <dasimov(a)earthlink.net <http://gosper.org/webmail/src/compose.php?send_to=dasimov%40earthlink.net>> wrote: > I wonder if there is a standard symbol in > math or physics or another field for one rotation. > > (Of course this is 2pi radians, but for certain > purposes it would be more convenient to refer > solely to the number of rotations, not radians.) > > If there is no standard symbol for this, I propose > a circle with a dot in the center. Comments? > > --Dan I don't like the circled dot. Isn't it already astro***ical for Sun? How about a circular little arrow. Then we'd have a cw and ccw sign option, and maybe even fractional turn and phase variations via lightface or dotted segments. uconv(rpm*min,1) 2 * %pi * radian uconv(%,hz*sec) hz * sec "This screw advances 1mm per RPM minute. Or is that per Hertz second?" --rwg NEOLASIOPTERAN PANTALOONERIES

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[math-fun] real numbers as infinite decimals
by James Propp 12 Feb '10

12 Feb '10

Do any of you know of books or articles that construct the real numbers (and their arithmetic) in terms of their binary (or decimal) expansions? I know of just two: the article "The real numbers as a wreath product" by Faltin, Metropolis, Ross, and Rota; and Gowers' web-screed "Real numbers as infinite decimals", aka "What is so wrong with thinking of real numbers as infinite decimals?". But I suspect there are others. Do you know of anyone else who has done anything along these lines? or even anyone who has given a conscientious definition of what's really involved when you add two infinite decimals and perform carries? Note that for this kind of analysis, 0.999... is not the same as 1.000..., even though both represent the same real number. (Here's a fun fact I haven't seen anywhere: if you add two (positive) infinite decimals, the only way their sum can end in infinitely 0's is if both summands do. Have you seen this before?) Any references or suggestions you can offer will be appreciated! Jim Propp

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Re: [math-fun] Symbol for rotation?
by N. J. A. Sloane 11 Feb '10

11 Feb '10

> Someone whose name I forget (do you recall Neil?) came by the OEISF booth in SF and in passing mentioned that he was having fun rewriting various things using "the correct value of pi", namely 2pi Yes, this was Bob Palais. Neil

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