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[math-fun] World Flag
by Jon Perry 11 Sep '03

11 Sep '03

With all this flag talk, let's imagine total harmony in the world, and a world flag is needed. What would it look like? Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] abcd
by Jon Perry 09 Sep '03

09 Sep '03

Can someone characterize the integer solutions to: ad + bc + bd = ac These correspond to pairs of complex numbers (a+bi)(c+di) such that the real part (ac-bd) is equal to the imaginary part (ad+bc). In Pari; { for (a=1,50, for (b=1,50, for (c=1,50, for (d=1,50, if (a*d+b*c+b*d==a*c,print(a","b","c","d)))))) } gives (e.g.) 10,8,9,1 10,8,18,2 10,8,27,3 10,8,36,4 10,8,45,5 Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] David Robbins
by James Propp 09 Sep '03

09 Sep '03

Forwarded from Greg Kuperberg (greg(a)math.ucdavis.edu) >I just found out, and I'm very sorry to report, that David Robbins died >yesterday (September 4). He was 60 or 61. As the Wall Street Journal >article explained, he was diagnosed with pancreatic cancer in May. >Clara Chan and Lynn Butler arranged a very nice conference for him in >June, in which I was happy to participate. Still, this was terrible >luck for him, and unfortunate for all of us. > >-- > /\ Greg Kuperberg (UC Davis) > / \ > \ / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/ > \/ * All the math that's fit to e-print * Jim Propp

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Re: [math-fun] more 51 star designs
by David Wilson 09 Sep '03

09 Sep '03

I would arrange 51 stars in a centered pentagonal arrangement. It would have a pretty 5-way symmetry, and would play on the lines of the stars. True, it's not rectangular, but then neither was the circle of 13 stars...

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[math-fun] Prime Graphs
by Jon Perry 08 Sep '03

08 Sep '03

Just for review, no comments required, (and apologies to PrimeForm for being slighly skew); http://www.users.globalnet.co.uk/~perry/maths/primegraph/primegraph.htm Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun]
by David Gale 08 Sep '03

08 Sep '03

The solutions of x^2 + y^2 = z^2 the well known "Pythagorean triples" goes back to Euclid. I'd like to know if anyone in the history of Diophantine equations has looked at the same problem with 2 replaced by -2. That is, find all solutions in integers of 1/x^2 + 1/y^2 = 1/z^-2. The solution is easy and rather nice. David

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Re: [math-fun] more 51 star designs
by asimovd＠aol.com 05 Sep '03

05 Sep '03

My ASCII skills fail me, but how about one star in the middle, surrounded by similar ellipses of either 6, 8, 10, 12, and 14 stars, where the ellipses are similar ones, and the stars on each underlying ellipse are equispaced w.r.t. arclength. The arrangement of stars has rectangular symmetry, with the "2 mod 4" ellipses of size 6, 10, 14 each having a pair of stars on the y-axis (to emphasize the horizontal elongation), and the "0 mod 4" ellipses of size 8 and 12 stars each having a pair of stars on the x-axis and (hence) a pair on the y-axis. (The same general idea can be tried using ellipses of 9, 10, 11, 12, and 13 stars, but this has less potential symmetry than the above.) --Dan

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[math-fun] England sees the light.
by Richard Schroeppel 05 Sep '03

05 Sep '03

> This is a problem that's worried me for quite some time : if and when there are 51 United States, then how should the resulting 51 stars be arranged on the "Stars and Stripes" flag? It's all very well to plan ahead, John, but I don't think Tony Blair could take the role reversal of being an American province. California would object to losing its #1 position in population and wackiness. And we're supposed to guarantee our states a Republican form of government -- what would become of the Queen? Besides, we don't even speak the same language. :-) [Or :-o) in the British spelling.] John has * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * for the 49 star flag. The 49 star flag was only current for a year (or two? ~1958). My memory is that the rows were staggered, like this: * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * But I'm not sure if the pattern was this way or left-right reversed -- ie, with the staggering being on odd rows instead of even. Rich rcs(a)cs.arizona.edu

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RE: [math-fun] The problem of the 51st state.
by Meeussen Wouter (bkarnd) 05 Sep '03

05 Sep '03

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O but horizontaly streched W. -----Original Message----- From: Meeussen Wouter (bkarnd) [mailto:wouter.meeussen@vandemoortele.com] Sent: vrijdag 5 september 2003 19:27 To: 'math-fun' Subject: RE: [math-fun] The problem of the 51st state. O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O -----Original Message----- From: Meeussen Wouter (bkarnd) [mailto:wouter.meeussen@vandemoortele.com] Sent: vrijdag 5 september 2003 19:04 To: MathFun (E-mail) Subject: RE: [math-fun] The problem of the 51st state. O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O loosenig at the corners? W. =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.

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RE: [math-fun] The problem of the 51st state.
by Meeussen Wouter (bkarnd) 05 Sep '03

05 Sep '03

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O -----Original Message----- From: Meeussen Wouter (bkarnd) [mailto:wouter.meeussen@vandemoortele.com] Sent: vrijdag 5 september 2003 19:04 To: MathFun (E-mail) Subject: RE: [math-fun] The problem of the 51st state. O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O loosenig at the corners? W. =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.

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