October 2009 - mathfun@mailman.xmission.com

[math-fun] NYT on Martin Gardner
by rcs＠xmission.com 22 Oct '09

22 Oct '09

Today's NYTimes has a short appreciation of Martin Gardner. http://www.nytimes.com/2009/10/20/science/20tier.html [If you haven't signed up for Exclusive(!) Online Access, try googling "For Decades, Puzzling People With Mathematics" to get the article.] I found it a bit thin, but it does recall the puzzle about how he was able to inspire so many kids to go into math. Maybe the key is having math as a hobby. Rich

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Re: [math-fun] linked spheres
by Dan Asimov 21 Oct '09

21 Oct '09

Rich wrote: << . . . separability test seems to work if we allow spheres as separators (instead of just allowing planes). >> Yes -- the family F = {all spheres and planes in R^3} is large enough to separate any two circles in R^3 that don't link. By the way, F has a natural topology homeomorphic to a punctured P^4 (4-dimensional projective space minus a point). --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] NYT on Martin Gardner
by Dan Asimov 21 Oct '09

21 Oct '09

My least favorite part of Scientific American is the "skeptic" column by Michael Shermer. I consider myself a hard-headed scientist. Yet I find his dismissal of anything that doesn't conform to the paradigm of present-day science to be arrogant and, in fact, not all that evidence-based. In the history of science, we repeatedly see new paradigms having developed, forcing realists to toss out old ones. But Shermer takes the view that if science doesn't know about something currently, then it can't exist. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] NYT on Martin Gardner
by Dan Asimov 21 Oct '09

21 Oct '09

He certainly influenced me, too, starting with one of the best presents I ever got, too -- the very same book. (But I got it at age 12, in 1959, and was under the impression the book had just come out.) I ate that stuff up. (Actually, I might have taken his 1956 book "Mathematics, Magic, and Mystery" out of the library a few years earlier.) --Dan << Martin Gardner definitely influenced me. One of the best presents that I ever got was in 1957, when I was 10, a friend of the family gave me a copy of the (brand new) book, "Mathematical Puzzles and diversions". I remember constructing all sorts of flexagons, etc. The sheer joy of all these puzzles went a long way to making me choose mathematics as a career. >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] NYT on Martin Gardner (and Scientific American)
by Eric Angelini 21 Oct '09

21 Oct '09

> Scientific American > No mathematical content whatsoever. ... gladly the French edition has today Jean-Paul Delahaye. I buy "Pour la Science" since #1 and remember well the gems of Martin Gardner -- and those of Douglas Hofstadter, Ian Stewart, Pierre Tougne (French columnist), etc. I think there always has been a maths column (more accurate : 6 pages every month!) in Pour la Science, starting in the early '70s, with no interruption. Philippe Boulanger, the former editor-in-chief was (is) a math-lover. ... Why the fine papers of Jean-Paul Delahaye aren't translate into English and published in SA is a mystery to me... Best, É. -----Message d'origine----- De : math-fun-bounces(a)mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Robert Baillie Envoyé : mercredi 21 octobre 2009 14:00 À : math-fun Objet : Re: [math-fun] NYT on Martin Gardner Martin Gardner was definitely one of the figures who influenced me. It's a tragedy that today's generation doesn't have a Martin Gardner to inspire them in math. (On the other hand, higher-income kids could have access to Mathematica, Maple, etc.) It's also pretty pathetic to pick up a recent copy of Scientific American and see what has become of that formerly great magazine... No mathematical content whatsoever. Bob Baillie ------------ rcs(a)xmission.com wrote: > > Today's NYTimes has a short appreciation of Martin Gardner. > > http://www.nytimes.com/2009/10/20/science/20tier.html > > [If you haven't signed up for Exclusive(!) Online Access, > try googling "For Decades, Puzzling People With Mathematics" > to get the article.] > > I found it a bit thin, but it does recall the puzzle about > how he was able to inspire so many kids to go into math. > Maybe the key is having math as a hobby. > > Rich > > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > _______________________________________________ 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] Mathcamp 2009 Qualifying Quiz
by Ray Tayek 21 Oct '09

21 Oct '09

http://www.mathcamp.org/quiz/quiz09.php --- co-chair http://ocjug.org/

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[math-fun] Diophantine equation
by Fred lunnon 21 Oct '09

21 Oct '09

It's always nice to have examples of geometrical configurations with rational parameters --- apart from anything else, they're useful for testing software. A polytore with square section edge 2, outer cuboid depth g, inner quadrangle height h, inner radius q, is planar just when h^2/(2-q^2) = g^2/(2-q)^2 + 1/2 but this equation appears to have no small rational solutions, at any rate when 0 < q < 1. Is it soluble over the rationals? WFL

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Re: [math-fun] linked spheres
by Dan Asimov 20 Oct '09

20 Oct '09

Linking is a fascinating phenomenon in topology, but the only chance of proving anything about it will require the use of a definition of linking. --Dan Fred wrote: << Paraphrased and extended from exercises 5.5--5.10 of Ian R. Porteous "Clifford Algebras and the Classical Groups" Cambridge (2000) --- surely familiar to those with a background in topology, but new to me. The circles and spheres are standard, rather than just homeomorphs. << Given disjoint circles C,D in 3-space, consider the (Gauss) map from vectors joining pairs of points, X on C and Y on D, to the unit sphere: (X, Y) -> (X - Y)/|X - Y|. Show that this map is surjective if and only if the circles are linked; and specify its fibres (pre-images). Show that two disjoint great circles in spherical 3-space are always linked. Specify precisely a criterion to decide whether two circles in 3-space are (not) linked. Design a simple, effective algorithm to decide whether two circles in 3-space are linked. Show that two spheres may be linked in 5-space, but not in 4-space or 6-space. Generalise (inductively?) to decide whether k-sphere and l-sphere in (k+l+1)- space are linked >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] linked spheres
by Fred lunnon 19 Oct '09

19 Oct '09

Paraphrased and extended from exercises 5.5--5.10 of Ian R. Porteous "Clifford Algebras and the Classical Groups" Cambridge (2000) --- surely familiar to those with a background in topology, but new to me. The circles and spheres are standard, rather than just homeomorphs. Given disjoint circles C,D in 3-space, consider the (Gauss) map from vectors joining pairs of points, X on C and Y on D, to the unit sphere: (X, Y) -> (X - Y)/|X - Y|. Show that this map is surjective if and only if the circles are linked; and specify its fibres (pre-images). Show that two disjoint great circles in spherical 3-space are always linked. Specify precisely a criterion to decide whether two circles in 3-space are (not) linked. Design a simple, effective algorithm to decide whether two circles in 3-space are linked. Show that two spheres may be linked in 5-space, but not in 4-space or 6-space. Generalise (inductively?) to decide whether k-sphere and l-sphere in (k+l+1)- space are linked. [The connection between such problems and the stated topic of section 5 --- the classification of real quadratic spaces --- itself constitutes an intriguing question, with regard to which I have yet to make progress.] Fred Lunnon

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[math-fun] math overflow
by Ray Tayek 18 Oct '09

18 Oct '09

a stackoverflow clone: http://mathoverflow.net/ from the faq: What kind of questions can I ask here? The primary criterion for determining whether a question is appropriate for Math Overflow is "is this of interest to mathematicians?" By a "mathematician," we mean a person whose primary occupation is doing mathematics. Of course, you should make your question detailed and specific, and write clearly and simply. Part of the goal of this site is to produce a repository of standard questions and answers that mathematicians have when they are exploring a new field; these "newbie" questions are welcome and even encouraged. Please look around to see if your question has already been asked (and maybe even answered!) before you ask. If you end up asking a question that has been asked before, that is OK and deliberately allowed. Other users will hopefully edit in links to related or similar questions to help future visitors find their way. It's also perfectly fine to ask and answer your own question, but pretend you're on <http://en.wikipedia.org/wiki/Jeopardy%21>Jeopardy: phrase it in the form of a question. Also, we recommend not answering your own question immediately since leaving the question "open" encourages other people to respond to it. You might discover that somebody else has an even better answer! ... --- co-chair http://ocjug.org/

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