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[math-fun] The Santayana Corollaries
by Thane Plambeck 20 Jun '03

20 Jun '03

"Those of us who forget the past are condemned to repeat it." (George Santayana) "Those of us who remember that it was Santayana who said, 'those of us who forget the past are condemned to repeat it,' are condemned to repeat it." (Plambeck) And: By the G.S. principle itself, even those of us who forget that it was George Santayana who said, "those of us who forget the past are condemned to repeat it," are condemned to repeat it... Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm

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RE: [math-fun] Geometry/topology question about planar graphs
by Andy Latto 17 Jun '03

17 Jun '03

> -----Original Message----- > From: John Conway [mailto:conway@Math.Princeton.EDU] e. > However, the > "Carpenter's Ruler" problem (are the plane embeddings of a > hinged ruler > interconvertible in this way, keeping the segment-lengths fixed) is > quite difficult - indeed I think it's still unsolved, This was finally solved, in the affirmative, by Erik Demaine, Robert Connelly, and Guenter Rote. http://theory.lcs.mit.edu/~edemaine/papers/Linkage/ > and the > corresponding assertion for arbitary graphs is false. Is there an easy-to-describe counterexample? Andy Latto andy.latto(a)pobox.com

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Re: [math-fun] Gardner's 6th book of games
by Jud McCranie 17 Jun '03

17 Jun '03

At 10:37 PM 6/16/2003, you wrote: > > Is Martin Gardner's "Sixth book of mathematical games/diversions" > > also known by a different name? Can someone tell me the name of the first chapter? Thanks.

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[math-fun] A sequence from Gardner's 6th book
by N. J. A. Sloane 17 Jun '03

17 Jun '03

Since there has been some discussion of this book, here is a sequence suggested by a problem in Chapter 4. Let S be a list of positive integers (with repeats allowed) such that every number from 1 to n can be obtained as a sum of 1 or 2 elements from S. (The minimal number of coins so that every amount from 1 through n can made using 1 or 2 coins) What are the values of a(n) = min size of any such S , for n = 1, 2, ...? (I don't know the answer.) M. G. says that a(100) <= 16, using S = { 1 3 4 5 8 14 20 26 32 38 44 47 48 49 51 52} found by Peter Wegner. NJAS

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Re: [math-fun] Gardner's 6th book of games
by asimovd＠aol.com 16 Jun '03

16 Jun '03

<< Is Martin Gardner's "Sixth book of mathematical games/diversions" also known by a different name? >> Quite likely, assuming it's still in print. (That's one of the two where my name appears.) Regards, Dan Asimov

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[math-fun] Gardner's 6th book of games
by Jud McCranie 16 Jun '03

16 Jun '03

Is Martin Gardner's "Sixth book of mathematical games/diversions" also known by a different name?

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[math-fun] Re: some puzzle sequences not in OEIS!
by David Wilson 16 Jun '03

16 Jun '03

17: 36, 864, 21060, 544320, ? If we index starting at 1, we have a(n) = a(n-1) ((n+10)(9n-12)/(5n-7)). This gives ? = 14968800. However, the subsequent term is noninteger. Yeah, it's ugly, what can I say.

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[math-fun] mystery constant .32810656687498
by R. William Gosper 15 Jun '03

15 Jun '03

is the largest nome, q, for which the closed curve x=theta_2(t,q), y=theta_1(t,q) is convex. Plouffe's inverter gives me 3281065668749782 = (m405) 1/NineConst^(1/2) Trying to parse "NineConst", I tried both squaring and reciprocating, and got "Not found"! And Simon seems to be away fom his email. ? --rwg

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[math-fun] Jaynes: "Probability Theory"
by Eugene Salamin 13 Jun '03

13 Jun '03

The book is now available. ISBN = 0521592712. Probability theory is developed as an extension of deductive logic to statements which are not true or false, but rather have degrees of plausibility. If you use statistical methods, and would like to understand how and why (and maybe even if) they work, you will want to read this book. Gene __________________________________ Do you Yahoo!? Yahoo! Calendar - Free online calendar with sync to Outlook(TM). http://calendar.yahoo.com

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[math-fun] Monckton & creation of hard tessellation puzzles
by Thane Plambeck 13 Jun '03

13 Jun '03

Monckton's Eternity Puzzle went bad on him, but is it possible to create similar puzzles with a reasonable expectation that no one is going to solve them over, say, a three year time frame, even with computers and extreme cleverness? It does seem to be a good idea to sell puzzles with big prizes for solutions if only one could know that they're attractive enough to sell and unlikely to be solved before the time limit... * * ** * * Old news from about 2000: Christopher Monckton thought he was on to a winner when he invented a new puzzle and offered 1 million pounds to the first person who solved it. Alas, his brainchild looks set to be a ruinous loser... http://showcase.posiweb.net/media/property01.pdf ********* Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm

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