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Re: [math-fun] Geometry/topology question about planar graphs
by asimovd＠aol.com 04 Jun '03

04 Jun '03

Suppose a finite graph G is embedded in the plane topologically. When can it be embedded so that all the edges are straight lines? Most interesting to me is the case where the straight-line embedding is obtained via a continuous deformation, through embeddings, of the original one. (And I'm most interested in the case where each of the graph's finite complementary components is bounded by exactly 4 edges.) --Dan

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[math-fun] problem at alum.mit.edu
by Richard Schroeppel 04 Jun '03

04 Jun '03

Several math-fun subscribers have addresses at alum.mit.edu. The MIT forwarder seems to have been a black hole for a few days, but is working at the moment. As near as I can tell, the missing messages were dropped. The recent archive is available from a web interface; see the List-Archive line in the message headers. Rich rcs(a)cs.arizona.edu

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[math-fun] nice product for (1+y)^(1/a)
by Joerg Arndt 04 Jun '03

04 Jun '03

I like this one: Let y Y =y T(y) = + - 1 a and a a a (1+Y ) a -(a+Y ) (1+Y ) a k k k Y =----------------- = --------- - 1 k+1 a a (a+Y ) (a+Y ) k k then ___oo 1/a | | (1+T(Y )) = (1+y) | |k=1 k Convergence is quadratic. The ansatz (T(y)="terms 1..(n-1) of Taylor series") also works for 1/\sqrt[a]{1+y} and gives products with n-th order of convergence. -- 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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[math-fun] Dedication and paragraph from Buzz Aldrin's Ph.D thesis
by Thane Plambeck 04 Jun '03

04 Jun '03

>From "Line-of-Sight Guidance Techniques for Manned Orbital Rendezvous," Edwin Eugene Aldrin's January 1963 Ph.D dissertation at MIT in Aeronautics and Astronautics, January 1963, with Dedication reading "In the hopes that this work may in some way contribute to their exploration of space, this is dedicated to crew members of this country's present and future manned space program. If only I could join them in their exciting endeavors!" Buzz got into the space program in 1966. Presumably this paragraph from page 88 wasn't held against him: "The basic conclusion to be drawn from all this discussion of rendezvous with targets in elliptic orbits is that, since the recommended techniques of intercepting such targets all stem from the similarity and analogies through transformation to intercepts of targets in circular orbits, all the succeeding analyses pertaining to intercepts between circular orbits are directly applicable through the same similarities and transformations to targets in elliptic orbits." Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm

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[math-fun] Test
by Allan C. Wechsler 03 Jun '03

03 Jun '03

I haven't been getting any math-fun messages for a few days, and I'm sending this message to see if I get it. Rich, if the list has been getting bounces from me, please try to contact me to let me know about it. Try acw(a)alum.mit.edu, and if this fails try Wechsler(a)world.std.com. If all else fails you can phone me at home, 617-484-3647, so I'll know things are awry and I'll try to debug it from my end. Thanks. -A

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Re: [math-fun] problem with prime gap proof
by asimovd＠aol.com 30 May '03

30 May '03

Hi, Thane. I haven't forgotten your suggestion about getting together, and it happens that Marc Le Brun (mlb) who lives in Marin is also interested. He tends to get to Palo Alto where his mother is convalescing, temporarily. In the unlikely event he can make it tomorrow around noon, could you also make it? Otherwise, how does next Saturday, June 7 look? --Dan

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[math-fun] Interesting use of number square
by David Wilson 30 May '03

30 May '03

I've never seen this trick before. What properties of the subsquares make this trick work? Would it be possible to perform this trick with a square that has distinct entries? Entries 1 through 64? http://www.mdani.demon.co.uk/stunt/may98s1.htm

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[math-fun] George Bush speaks on Mathematics (fwd)
by Richard Guy 30 May '03

30 May '03

---------- Forwarded message ---------- Date: Wed, 28 May 2003 13:54:35 -0600 From: Ernest Enns <enns(a)math.ucalgary.ca> To: dept <dept(a)math.ucalgary.ca> Subject: George Bush speaks on Mathematics Apparently a teacher has been arrested in the UK in possession of compasses, protractor, and straight edge. It is claimed he is a member of the Al Gebra movement bearing weapons of math instruction.

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Re: [math-fun] [seqfan] Signatures of irrational numbers
by asimovd＠aol.com 30 May '03

30 May '03

Marc, I just disovered that AOL has been hiding the name accompanying the e-address under a little button called "Details". By clicking on that and reading through about 30 lines of tiny type, I found that I've been misspelling your first name. I hope you will accept my apologies. And I hope I will hear from you. --Dan

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Re: [math-fun] flame oops
by asimovd＠aol.com 30 May '03

30 May '03

Gene writes: << There are also wonderful resources hidden away in books; the problem is identifying the few good ones among all the trash. Something we could do to help the bright students stuck in lousy schools is to prepare reading lists of good books and post them on the internet. The lists should include politically incorrect material, not only because much that is scientifically correct is politically incorrect, but also because then the schools might then try to have the lists banned, and that would generate publicity that no amount of money could buy. >> I'm totally in favor of trying to improve the education of T.C. MITS (the common (hu)man in the street) and like the direction Gene's thought are running in. I am strongly against trying to maintain political correctness merely for the sake of not offending anyone. But let us suppose that, repeatedly, unbiased and well-performed studies of individuals of group A (e.g., an ethnicity or gender) showed them to be statistically less innately able to do task X than individuals not in group A. Perhaps that would be interesting information, but it strikes me as something that could far more likely do more harm than good if widely publicized. In particular, it would prejudice the easily-prejudiced (and that includes a lot of people) against anyone of group A, despite the fact that a very large number of group A may be vastly well-qualified at task X. * * * And I'm against "demonizing" plutonium or anything else, yet it is a very dangerous substance (I've heard convincing claims that a millionth of an ounce of Pu in one's lungs is virtually certain to cause lung cancer within 20 years). And as of about 1980, there were about 20 pounds of the stuff unaccounted for from our stockpiles of nuclear material. Now, with the breakup of the U.S.S.R. and Iraq behind us, who knows how much more is also unaccounted for. Without "demonizing" anything, I am realistically concerned that some rogue individuals or groups would gladly accumulate dangerous materials and use them to harm innocent people. And even non-rogue individuals are susceptible to bribes, threats, and simple mistakes. --Dan

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