September 2003 - mathfun@mailman.xmission.com

RE: [math-fun] The problem of the 51st state.
by Schroeppel, Richard 05 Sep '03

05 Sep '03

The 46-star field is like the 48 field, with rows 2 & 5 having only 7 stars and being centered. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * I recall seeing a different design somewhere: * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Sort of "no nonsense". This must have been inspired by the recent science articles about the 3-D version of the problem for small clusters of atoms. Rich -----Original Message----- From: John Conway To: math-fun Sent: 9/5/2003 9:37 AM Subject: Re: [math-fun] The problem of the 51st state. On Fri, 5 Sep 2003, Thane Plambeck wrote: [clip] > I've thought the 46 star flag shown at the URL below must not be the best possible. I don't know how to read that - can you roughly draw or describe it for me? JHC _______________________________________________ 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] 12 exponentials conjecture
by Jon Perry 04 Sep '03

04 Sep '03

wrt. http://mathworld.wolfram.com/SixExponentialsTheorem.html and http://mathworld.wolfram.com/FourExponentialsConjecture.html what is known if x1,x2 are linearly independent complex numbers, as are y1,y2 and z1,z2. Then must one of; e^x1y1, e^x1y2, e^x2y1, e^x2y2, e^x1z1, e^x1z2, e^x2z1, e^x2z2, e^y1z1, e^y1z2, e^y2z1, e^y2z2 be transcendental? 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] Perry's Observation
by Jon Perry 02 Sep '03

02 Sep '03

According to; http://www.users.globalnet.co.uk/~perry/maths/fourcolour/fourcolour.htm the 3-sphere can be constructed in plastic but not in wood. What other mediums render the 3-sphere impossible, and what other PO objects can not be constructed in wood? 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] Re: inversion in finite field ~= fourier transform?
by Mike Stay 01 Sep '03

01 Sep '03

I wrote: >In GF(2^n), inversion behaves very much like a >change between conjugate observables and made a vague comparison to a Fourier transform; after a little more thought, I guess it's more like convolution, since it's the sum of products going in opposite directions. So (x+h)^-1 = x * h = sum over even k ( x^{N-k} h^k ) where N=2^n-2. I guess I need to figure out whether this definition of convolution gives anything useful... -- Mike Stay staym(a)clear.net.nz http://www.xaim.com/staym

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[math-fun] astroid: 3 recipes and a question
by R. William Gosper 01 Sep '03

01 Sep '03

For a circle of radius r rolling inside the unit circle: 1) r=1/4: trajectory of point on circumference. 2) r=3/4: trajectory of point on circumference. (opposite dir) 3) r=1/2: boundary of area swept by diameter. All draw x^(2/3) + y^(2/3) = 1. What density function rho(r) must a planet have so that an astroid is a brachistochrone? --rwg

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