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Search: id:A130795
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| A130795 |
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Multiaxial coordinate vectors normalized at Theta=0 and Phi=0 and rounded to the nearest integer ( "n" factor is added to make the integers show up better): based on cyclotomic angles for solving polynomials of the type x^n-1=0. |
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+0
2
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| 1, 2, 2, 3, 1, 1, 4, 0, 4, 0, 5, 0, 3, 3, 0, 6, 2, 2, 6, 2, 2, 7, 3, 0, 6, 6, 0, 3, 8, 4, 0, 4, 8, 4, 0, 4, 9, 5, 0, 2, 8, 8, 2, 0, 5, 10, 7, 1, 1, 7, 10, 7, 1, 1, 7
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The multidimensional coordinates give generalized cylinders in n dimension. The 3-dimensional example is a right cylinder : {x, y, z} = {Cos[p] Cos[t], Cos[p + (2 Pi)/3] Cos[(2 Pi)/3 + t], Cos[p + (4 Pi)/3] Cos[(4 Pi)/3 + t]}
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REFERENCES
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A torus based on the n=3 version of these coodinates was an MAA sticker by Paul Bourke: http://local.wasp.uwa.edu.au/~pbourke/surfaces_curves/tritorus/index.html
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FORMULA
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a(theta,phi,i,n)=Cos[theta + 2*i*Pi/n]*Cos[phi + 2*i*Pi/n]; t(n,i)=Round[n*a(0,0,i,n)]
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EXAMPLE
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{1},
{2, 2},
{3, 1, 1},
{4, 0, 4, 0},
{5, 0, 3, 3, 0},
{6, 2, 2, 6, 2, 2},
{7, 3, 0, 6, 6, 0, 3},
{8, 4, 0, 4, 8, 4, 0, 4},
{9, 5, 0, 2, 8, 8, 2, 0, 5},
{10, 7, 1, 1, 7, 10, 7, 1, 1, 7}
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MATHEMATICA
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a[t_, p_, i_, n_] = Cos[t + 2*i*Pi/n]*Cos[p + 2*i*Pi/n]; Table[Table[Round[n*a[t, p, i, n]], {i, 0, n - 1}], {n, 1, 10}] /. t -> 0 /. p -> 0; Flatten[%]
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CROSSREFS
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Adjacent sequences: A130792 A130793 A130794 this_sequence A130796 A130797 A130798
Sequence in context: A066422 A092779 A078827 this_sequence A071435 A119428 A051521
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L Bagula (rlbagulatftn(AT)yahoo.com), Jul 15 2007
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