September 2005 - mathfun@mailman.xmission.com

[math-fun] Atlas Replies + Help
by David Wilson 26 Sep '05

26 Sep '05

In deference to the Math-Fun and Seqfan lists, I would ask that you address any questions to about the Atlas directly to me at davidwwilson(a)comcast.net, and not copy to math-fun or seqfan lists. I am still looking for a free or nominal-charge mailing list server for an Atlas mailing list. -------------------------------- - David Wilson

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[math-fun] Geometry book "Divine Proportions"
by Joerg Arndt 26 Sep '05

26 Sep '05

A colleague has pointed me to the book "Divine Proportions: Rational Trigonometry to Universal Geometry" by N J Wildberger (Assoc Prof UNSW Sydney) See http://wildegg.com/products.htm I am not into geometry but some people on the list surely are. Therefore this posting. -- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.

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RE: [math-fun] Sex, Lies and Government Conducted Surveys
by dasimov＠earthlink.net 26 Sep '05

26 Sep '05

David Gale writes: << . . . The objective of the survey is to get information on public health concerns, fertility, sexually transmitted disease, etc. However I bring it up here because it contains the most glaring examples I have yet seen of published inconsistency. It's the well worn story that males have many more "sexual partners" than females. Interested people should look at the report. For example, Tables 10 and 11 of the survey show that the median number of partners "in lifetime" for males over forty is 8 while that for females is 3.8. To immediately recognize the inconsistency imagine the same survey with but with the words sexual partners replaced by spouses. For more of the same look at Figure 6 on page 6. More inconsistency: when men and women are asked for the number of partners over the past 12 months, Tables 1 and 2, the numbers come out the same, within epsilon. . . . >> I'm not entirely sure what the researchers were supposed to do -- they are merely reporting the results of their survey and attempting to interpret the inconsistencies, which to their credit they acknowledge. It is a well-known fact that people's unverifiable self-descriptions are biased toward making themselves look good (or at least better than reality), and so are prone to inconsistency. Many simple explanations are possible. One is the truism that it is often considered an indication of virility for men to have had numerous sexual partners (up to a point), whereas for women this is often frowned upon. Hence, men would have an incentive to report higher, and women lower, numbers, than actual fact. (But when only the past year is considered, the numbers are relatively small, so there may be less incentive to mis-report -- and also a clearer memory of what actually happened.) I don't get why replacing "sexual partners" with "spouses" makes any inconsistency clearer. It seems easy to believe that unmarried sexual behavior tends to be different from married. --Dan

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RE: [math-fun] Multiplicative Magic Squares
by Schroeppel, Richard 26 Sep '05

26 Sep '05

There's a standard proof that the center of a 3x3 magic square is K/3, where K is the row sum. (Add up the four lines through the center, subtract the whole square.) Of course this works for multiplication too, so the magic product is always the cube of the center. There's a collection of similar results for a 4x4 square, such as "the sum of the four corners is K" etc. Although the arguments offered so far are plausible, I think a bit more proof is in order before claiming minimality of the various squares. Maybe a program? There aren't that many potential products < 5040 with 16 divisors, and we can also require the exponents in the prime factorization form a descending staircase. Allowing 0 as an entry doesn't seem helpful. I suspect that allowing negatives will turn out to be equivalent to the positive case with duplications allowed (but not triplications & up). But I don't see the proof that minus signs can always be attached to a positive square in a consistent way. Rich rcs(a)cs.arizona.edu -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov(a)mailman.xmission.com [mailto:math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com] On Behalf Of Christian Boyer Sent: Thursday, September 22, 2005 9:02 AM To: 'math-fun' Subject: RE: [math-fun] Multiplicative Magic Squares Of course replace "magic sum" by "magic product", twice in my previous message... -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr(a)mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 22 septembre 2005 16:30 À : 'math-fun' Objet : RE: [math-fun] Multiplicative Magic Squares In his old book on recreative mathematics, Boris Kordiemski described exactly the Michael's method (using two latin squares) for 4x4 multiplicative squares. He also described a method for 3x3 multiplicative squares: a b² a²b a²b² ab 1 b a² ab² With a=2 and b=3, you get 2 9 12 36 6 1 3 4 18 Magic sum = 216 (*). It is the smallest possible multiplicative square. In 1667 (a long time ago...), Arnauld gave a 3x3 multiplicative square. Perhaps the oldest published multiplicative square? Using powers of 2, its magic sum was bigger : 4096. Christian. (*) 216 is also the smallest cube being also sum of three cubes. 216 = 6^3 = 3^3 + 4^3 + 5^3 _______________________________________________ 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] Frost visits the Gulf on a blustery evening
by Hilarie Orman 26 Sep '05

26 Sep '05

> >> A front-page Sat., Sept. 17 story on the NY Times website, > >> found at http://snipurl.com/hqxi, claims that FEMA has > >> delivered 177 million tons of ice to Louisiana, Mississippi and > >> Alabama in the aftermath of hurricane Katrina. Some say the Gulf will end in water, Some say in ice. >From what I've witnessed of Katrina, I hold with those who favor FEMA. But if it had to perish twice, I think I know enough of weight, To say that for destruction ice Is also great And would suffice. Hilarie, With apologies to RF.

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[math-fun] Announcement: Atlas of Natural Numbers
by David Wilson 26 Sep '05

26 Sep '05

In the near future, I intend to begin serious development on my Atlas of Natural Numbers, a web site devoted to collecting and organizing interesting information about individual natural numbers. As a first step, I would like to establish a mailing list for the Atlas. Any information on a good free mailing list server would be appreciated. -------------------------------- - David Wilson

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[math-fun] Re: Web help
by David Wilson 26 Sep '05

26 Sep '05

Sorry, I was not sufficiently detailed in my last message on this subject. I am in the process of constructing a web-based Atlas of Natural Numbers. This project is partly motivated by love of the subject, and partly motiviated by the need to acquire some demonstrable Web tech skills if i ever hope to break back into the computer business. At the present time, I am using a Perl converter program to generate HTML pages from an ad-hoc backend database. I have installed a local Apache web server that allows me to view my pages as a virtual site on my local machine. But as the amount of data has grown, the Perl converter is starting to bog down, and I realize the need for a more standard database such as SQL or XML (I prefer the latter). I am, however, running into technical snags. I have not been able to successfully use a CSS style sheet to view XML documents, and I don't know what the problem is, so I am stopped. And it may be that I need something more powerful than CSS to get what I want, such as XSLT or PHP, but I'm not a web design geek (yet). So I would like to get in touch with someone who is web design savvy. I know that a few people in math-fun and seqfan have impressive sites, like Ed Pegg. I promise to (try) not to be a pain to whomever takes me up on this. Thanks. - Dave Wilson

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[math-fun] Serge Lang has died.
by dasimov＠earthlink.net 25 Sep '05

25 Sep '05

Today's New York Times website carries an obituary: http://www.nytimes.com/2005/09/25/national/25lang.html --Dan

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[math-fun] Web help
by David Wilson 25 Sep '05

25 Sep '05

I have collected a lot of information about numbers that I am trying to put together into a website. I need some help with basic web design and web tech questions. Would anyone in math-fun or seqfan be willing to help me out there? -------------------------------- - David Wilson

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Re: [math-fun] 177 million tons of ice???
by dasimov＠earthlink.net 23 Sep '05

23 Sep '05

Stev Harris writes: << [Death by deuterium] might make a good cerebral mystery for a student text: a person with full control of an elderly relative deuterates them to death over a couple of weeks to a month (which would take about 50 kg of heavy water at $300 a kg, but nevermind). Forensics thinks the person died of some strange disease or poison, but can't identify one (since they don't routinely do any tests to identify D!). The detective only recognizes something's amiss when the bad guy offers him ice in his lemonade, and has forgotten to dump the ice in the icebox, which is made from heavy water. Detective notices the ice SINKS in his glass. Hmmmm. >> I think this might make a good mystery, period! I love the punch line. (But after years of watching Law & Order, it seems clear that homicide detectives (at least in NYC) have a rule never to accept refreshments offered them when interviewing a witnesses at their homes.) Still, there must be some way around this. --Dan

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