Re: [math-fun] pizza packing
Are the exact polynomials available? --rwg I love that m=n sequence 2, 2, 1.942, 1.997, 1.951, 2, 1.942,... State lasciando il settore italiano --------------- on the off-chance that some of you like recreational packing problems, this month's math magic problem is about efficient packings of pizza slices: http://www2.stetson.edu/~efriedma/mathmagic/0112.html erich
I love that m=n sequence 2, 2, 1.942, 1.997, 1.951, 2, 1.942,...
it's unlikely the values are the best possible for n>=6.
Are the exact polynomials available?
for n=4, s=1+cos(t)-sin(t)+tan(t) at the t value that minimizes s. for n=5 and n=6, they were computed by david cantrell, and i have a mathematica notebook that probably contains some clue, but i'm afraid i can't decipher it. i'll be glad to e-mail it to you if you want. erich
BillG>> I love that m=n sequence 2, 2, 1.942, 1.997, 1.951, 2, 1.942,... The value s = 2 for n = 7 is not optimal. Surely, after n = 3, we always have s < 2. Erich> it's unlikely the values are the best possible for n>=6. The packing for n = 6, due to Maurizio Morandi, is plausibly optimal, IMO.
Are the exact polynomials available?
for n=4, s=1+cos(t)-sin(t)+tan(t) at the t value that minimizes s.
for n=5 and n=6, they were computed by david cantrell,
Only for n = 5 actually. And even though I produced the Mathematica notebook to which Erich refers, I have no idea what the exact polynomial would be, but can assure you that it would be utterly horrid. David
and i have a mathematica notebook that probably contains some clue, but i'm afraid i can't decipher it. i'll be glad to e-mail it to you if you want.
participants (3)
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Bill Gosper -
dwcantrell＠comcast.net -
Erich Friedman